A/C off due to high engine tempureature

If the temperature gauge stays on cold, then we need to start with checking for codes.

It sounds like we have a perceived issue rather than the engine actually overheating.

Have you ever had the engine get so hot that it shuts off or boils coolant out of the bottle?

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

You actually have two engine coolant temperature sensors, so we need to start with codes and see what is there.

Then we need to check the operation of these sensors. The best way to do that is check the voltage on both wires for each sensor.

https://www.2carpros.com/articles/how-to-check-wiring

I am attaching the wiring diagram below that will help with this but let's start with codes and go from there. If you don't have a code reader, then you can stop by most parts stores as they will pull them free of charge. Thanks