Why would a 2006 Nissan Altima blowing hot air from the air conditioning system?

Question edited for clarity, add maker and typo 'Alima'.
Question moved from AC Cars, maker of the AC Cobra.

Let's deal with the overheating engine first.

You may have air in the system

https://www.fixya.com/cars/r29872074-vehicle_cooling_system_no_heat

Or is may be the coolant temperature sensor not turning the radiator fan on, fan relay, or the fans themselves.

There are a number of things that could be the issue. Here is the fuse box diagram. You have two fuses and a relay covering the Air Conditioning.

https://fuse-box.info/nissan/nissan-altima-l31-2002-2006-fuses-and-relays

The system may need refrigerant gas, but check the fuses and relay first as it sounds electrical because the green signal light isn't on..

Much of the issues you have are ultimately controlled by the Body Control Module and you may have a computer communication issue. The only way to diagnose that is by an auto electrician with a pro grade scan tool computer to check modules, sensors and the computer networks. This is not a $125 scanner, they cost between $3.5k to $5k.

Go to auto zone and buy a recharge kit follow the instructions buy the large can of refrigerant,it is very simple to do

Well the car must have a wide open throttle relay that disables the compressor clutch under a load.
it is most likely stuck or not working it most likely gets a signat from the ecm to cut of power to the ac clutch

Someone will need to find out if the compressor clutch is failing, or if it is loosing power due to a pressure switch or other problem.
A faulty relay or switch could get hot and switch off power to the compressor.

could be your switch, or you have a freon leak and there is no freon in the system. open hood and watch the ac pump and have them turn on and off the ac. if in engages then it is probably freon. if it doesn't check ac fuses.

2000 Nissan Altima Heater Air Condition Section HA 76 pages Here is factory service repair manual for your vehicle . Do you know how to do testing on these system ? Automotive electrical system testing ? How to read a wiring diagram ? When hot outside is the inlet pipe to evaporator freezing up ? Do you know where this is , under the hood in the engine compartment at the fire wall . What are gauge readings , Is the compressor engaging ? Were any switches replaced ? Ambient temp. , thermal transmitter switch . pressure etc...

air conditioning is cold then it gets warm. compressor doesnt run very long

verify the radiator fans, fuses, relays of fans. when you turn on the a/c all the radiator fan turn on too, if not you have a problem with it.

your high pressure switch is faulty. the part is about 50$

Hi!
It appears we have an Air lock scenario and you will need to perform a system Bleed.
Park the vehicle on level ground, when cold remove coolant filler cap, start engine and leave to idle, turn heater on full and blower to max. When engine reaches operating temperature watch and listen near coolant filler, keep clear as gurgling and hopefully a boil over should occur. Top up with very warm coolant and wait as it may do it again.
Check for heat inside vehicle if warm replace coolant cap but keep an eye on temperature gauge as the ~Air lock may have moved on from heater matrix/core so proceedure needs to be carried out again from COLD.

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Paul 'W' U.K