Not cooling as before - 2003 Toyota Corolla

That vehicle has 3 relays ,not just 2 . Two cooling fans .

Cooling Fan Control
The engine cooling fan system consists of two electrical cooling fans and three fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G103.
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan s/p relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3-second delay, the PCM supplies a ground path for the cooling fan 2 relay and the cooling fan s/p relay through the high speed cooling fan relay control circuit. This energizes the cooling fan s/p relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
The PCM commands Low Speed Fans on under the following conditions:
• Engine coolant temperature exceeds approximately 106°C (223°F).
• A/C refrigerant pressure exceeds 1310 kpa (190 psi).
• After the vehicle is shut off if the engine coolant temperature at key-off is greater than 140°C (284°F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.
The PCM commands High Speed Fans on under the following conditions:
• Engine coolant temperature reaches 110°C (230°F).
• A/C refrigerant pressure exceeds 1655 kpa (240 psi).
• When certain DTCs set.


https://www.youtube.com/watch?v=pI4pH66TdDk

Usually a bad relay. See this post on GM relays and cooling fans

https://ricksfreeautorepairadvice.com/car-overheating/

It means you should take your vehicle to a qualified repair shop , at least that's the car makers thought .
A/C Off For Engine Protection
Refer to Cooling System Description and Operation
Cooling Fan Control
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) or engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 maxifuse?® through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation, the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 2 relay and the cooling fan relay through the high speed cooling fan relay control circuit. This energizes the cooling fan relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 maxifuse?® on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
Are the radiator fans coming on ? You mite take it an have it checked for DTC'S - diagnostic trouble code's .

A/C Off For Engine Protection
Refer to Cooling System Description and Operation

DTC P1258: Engine Coolant Overtemperature - Protection Mode Active.
This is something you need to take to a qualified repair shop .
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) or engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 maxifuse® through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation, the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 2 relay and the cooling fan relay through the high speed cooling fan relay control circuit. This energizes the cooling fan relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 maxifuse® on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.

Wiring for cooling system ? You mean cooling fans ? 1.6 ? This vehicle has 1.8 L or 1.9 L . This cooling system has two electric cooling fans . Three relays , cooling fan power relay , cooling fan hi speed relay an the low speed cooling fan relay. The powertrain control module controls these relays. Go here http://bbbind.com/free_tsb.html free wiring diagrams .

In the engine compartment fuse block. Look at positions 7 and 8. There should be a diagram under the lid.

there is 2 fuses that you have to check
one will be in the big fuse assembly in the engine bay, the other probably in the fuse assembly in the cab
If they prove ok then it is possible that the coolant temperature SENSOR is faulty and needs replacing
don't confuse it with the temperature sender which operates the temp gauge.

The engine cooling fan system is controlled by the body control module (BCM) and the powertrain control module (PCM) or engine control module (ECM). The BCM performs the calculations as to how long, when and what speed the cooling fans should turn on. The BCM then sends a class 2 message to the PCM/ECM to engage the cooling fan relays. If there is a malfunction with the BCM, the PCM/ECM will control the engine cooling fans independently. The engine cooling system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the PCM/ECM to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood accessory wiring junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan 2 relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 3 or S/P relay and the cooling fan 2 relay through the high speed cooling fan relay control circuit. This energizes the cooling fan 2 relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
The BCM and PCM/ECM command Low Speed Fans on under the following conditions:
?€¢
Engine coolant temperature exceeds approximately 106?°C (223?°F).

?€¢
A/C refrigerant pressure exceeds 1 310 kPa (190 psi).

?€¢
After the vehicle is shut off if the engine coolant temperature at key-off is greater than 140?°C (284?°F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.

The BCM and PCM/ECM command High Speed Fans on under the following conditions:
?€¢
Engine coolant temperature reaches 110?°C (230?°F).

?€¢
A/C refrigerant pressure exceeds 1 655 kPa (240 psi).

?€¢
When certain DTCs set.

The three relays are located in the under hood fuse / relay box ! You need to have it checked for DTC'S -diagnostic trouble codes ! An you need a GM Tech 2 scan tool !
This diagnostic procedure supports the following DTCs:
?€¢
DTC P0480 Cooling Fan 1 Relay Control Circuit

?€¢
DTC P0481 Cooling Fan 2 and 3 or S/P Relay Control Circuit

?€¢
DTC P0691 Cooling Fan 1 Relay Control Circuit Low Voltage

?€¢
DTC P0692 Cooling Fan 1 Relay Control Circuit High Voltage

?€¢
DTC P0693 Cooling Fan 2 and 3 or S/P Relay Control Circuit Low Voltage

?€¢
DTC P0694 Cooling Fan 2 and 3 or S/P Relay Control Circuit High Voltage

1. Install a scan tool.
2. Turn ON the ignition, with the engine OFF.
3. With a scan tool, command the Fans Low Speed ON and OFF.

Do the low speed engine cooling fans turn ON and OFF with each command?
Go to Step 3
Go to Step 4

3

Important:: A 3 second delay occurs before the powertrain control module (PCM)/engine control module (ECM) changes the cooling fan speed.
With a scan tool, command the Fans High Speed ON and OFF.
Do the high speed engine cooling fans turn ON and OFF with each command?

Are you talking about the radiator fan? How hot does the engine get in degrees F? Some makes and models, the radiator fan won't turn on till about 220 degrees F. Check for applicable trouble codes, see if any code that refers to the radiator fan circuit or coolant temp sensor? Some of the national brand auto stores will check codes for free.

Of course, as far as overheating in general, you have the thermostat--water pump and other possible issues. Are you losing coolant?

The computer turns on the fan. Based on sensors from the motor.
DTC P0480 - COOLING FAN CIRCUIT

Circuit Description

The cooling fan is controlled by PCM through the fan relay based on inputs from ECT sensor, IAT sensor, A/C selector switch, A/C refrigerant pressure switch and vehicle speed sensor. PCM controls cooling fan by grounding cooling fan control circuit which turns on cooling fan relay.

The fan relay will be commanded on when ECT reaches 223°F (106°C) or greater, A/C is requested or vehicle speed is less than 38 MPH. Cooling fan relay will also be commanded on regardless of vehicle speed when a DTC is set requesting cooling fan to be on, ECT is 304°F (151°C) or greater, or A/C refrigerant pressure is high. Cooling fan may also be commanded on when engine is not running, on certain conditions.

Conditions for setting DTC:

Battery voltage greater than 9.5 volts.

Cooling fan fault line detects a malfunction for 6 seconds.

1. Check cooling system. Ensure coolant level and belt tension are correct. Adjust/repair as necessary. After repairs, go to step 23). If no adjustment or repairs were required, go to next step.

2. Turn ignition on, with engine off. Using scan tool, check if cooling fan is operating with ECT at less than 209°F (98°C). If cooling fan is off, go to next step. If cooling fan is on, go to step 4).

3. Command cooling fan relay on. If cooling fan operates, go to step 23). If cooling fan does not operate, go to step 5).

4. Turn ignition off. Disconnect PCM harness connector. If cooling fan turns off, go to step 23). If cooling fan does not turn off, go to step 6).

5. Disconnect cooling fan relay harness connector. Using a test light connected to ground, probe battery feed circuits in relay harness connector. If test light illuminates on both terminals, go to step 7). If test light does not illuminate on both terminals, go to step .

6. Disconnect cooling fan relay harness connector. With test light connected to ground, probe battery feed circuit in relay harness connector. If test light illuminates, go to step 9). If test light does not illuminate, go to step 10).

7. Connect a jumper wire between cooling fan relay battery feed and cooling fan battery feed circuit. If cooling fan operates, go to step 11). If cooling fan does not operate, go to step 12).

8. Repair open in battery feed circuit. After repairs, go to step 23).

9. Repair short to voltage in cooling fan battery feed circuit. After repairs, go to step 23).

10. Connect test light battery voltage and probe cooling fan control circuit. If test light illuminates, go to step 13). If test light does not illuminate, go to step 21).

11. Connect test light to battery voltage and probe cooling fan control circuit. Using scan tool, command cooling fan on. If test light illuminates, go to step 14). If test light does not illuminate, go to step 15).

12. With jumper wire still connected, disconnect cooling fan harness connector. Using test light connected to ground, probe cooling fan battery feed circuit. If test light illuminates, go to step 16). If test light does not illuminate, go to step 17).

13. Repair short to ground in cooling fan control circuit. After repairs, go to step 23).

14. Check terminals to cooling fan relay. Repair as necessary. After repairs, go to step 23). If terminals are okay, go to step 21).

15. Check cooling fan control circuit for open or poor connection. Repair as necessary. After repairs, go to step 23). If circuit or connection is okay, go to step 22).

16. Connect test light to battery voltage and probe cooling fan ground circuit. If test light illuminates, go to step 1. If test light does not illuminate, go to step 19).

17. Repair open or poor connection in cooling fan ignition feed circuit. After repairs, go to step 23).

18. Check for poor connections at cooling fan harness connector. Repair as necessary. After repairs, go to step 23). If connections are okay, go to step 20).

19. Repair open or poor connection in cooling fan ground circuit. After repairs, go to step 23).

20. Replace cooling fan motor. After replacing cooling and motor, go step 23).

21. Replace cooling fan relay. After replacing relay, go to step 23).

22. Replace PCM. Program replacement PCM using required equipment. After replacing PCM, go to next step.

23. Turn ignition on, with engine off. Command cooling fan on. If cooling fan operates, system is okay. If cooling fan does not operate, repeat step 1).