What causes the car engine to overheat?
The amount of load it is hauling, whether inside or like pulling a trailer. Also using the air conditioning while going up very long grades on the roadway will cause overheating as the engine has to work harder going uphill and adding the drag of the air conditioning pump only makes that more difficult.
Turning the heat on would actually lower the engine temperature. It's a well known trick if your car starts to overheat. Having the A/C on causes a power loss to operate the compressor, which would also cause engine temperature to go up due to the hot air from the condensor going through the radiator.