97 Hyundai Lantra. Temp gauge shows engine very hot

Not normally. If the heat temp GAUGE shows hot and the A/C blows warm you could actually be having a hot engine.situation. The heat GAUGE is controlled by the TEMP SENDER UNIT and has no connection with the A/C other than the A/C condenser rides in front of the radiator and catches all the debris first which can plug up the air flow to the radiator and cause the temp gauge to climb. If the A/C condenser is plugged by dirt and debris the Freon can't get cooled down enough to cool the cabin temp very well.
My suggestion would be to back wash the radiator and condenser. Use a high pressured garden hose and from the engine bay squirt the hose through the radiator and the condenser both to remove what you can't see. Be very careful not to bend the cooling fins of either the radiator or the condenser.

If your saying 165 degrees F, that isn't right, in my opinion. With a 5.7L engine and 195 degree thermostat, I want to see over 200 degrees F on a fully warmed -up engine.
Are the heater hoses hot?

Not necessarily. The vehicle, in motion, has enough air flow through the radiator that the fan is usually not needed. The fan will run if the vehicle sits and idles for a while and the coolant temp rises since there is no air flow through the radiator. If you are worried about fan operation, there are two things to check. The fans will ALWAYS come on if the A/C is turned on. That is because the fans pll air through the A/C coil in front of the radiator. Air must flow through that at all times or pressure in the A/C lines will get too high. So test that circuit simply by running the engine and turning on the A/C. If the fans run, that part works. Now turn the A/C off. Let the engine run until the temp gauge gets to around 200-220 degrees F. The fan should come on about this time and run until the temp drops to about 190. This cycle will continue to keep the coolant from getting too hot. If the temp gauge gets into the red area and the fan has not come on, shut down the vehicle immediately to prevent engine overheating, and then troubleshoot that portion of the fan circuit.

Have you lost cooling fluid, or oil? If fluid is non existant, the Temp gague may not have enough information, or it hasn't been operating for some time, especially if there is no cooling fluid.

It has to do with engine temperature. Was this the first run after the rebuild?

If the temp gauge shows normal, you would not expect the fan to be on much. It is controlled by the coolant temp sensor. If the fan will not come on when the car gets really hot, it is possible this sensor has failed.

It is normal for both AC and cooling fans to be on when you turn on AC to cool setting.

Using your tatco code reader, select current data (real-time data) and select engine coolant temp sensor (ECT). Run engine to operating temperature (A/C off). Monitor the temp reading - when the temp reaches approx 204 deg farenheit, the fans should kick on, after the temp drops to approx 198 deg farenheit, the fans should turn off. The fans are controled by the ECM (Engine Control Module). The ECM controls the cooling fan relays.

inside the fuel tank ,gauze filter on bottom of pump if it runs ok leave well alone

Let the truck run for about 15 minutes. If the engine temperature does not come up turn the heater on and check to see if the air coming out is hot or cool. If it is hot the engine's thermostat is operating fine and most likely the problem is with the temperature sending unit for the gauge. If the air is cool the thermostat is stuck open. Try replacing the thermostat if the air is cool.

Starter's goin' out.

-bigMIKE