Does the thermostat have anything to do with the A/C working then not working? I was told it did, but it makes no sense to me. When the temperature gauge works, the A/C does, when it does not the A/C does not?
Well, the thermostat allows the passage of water to the radiator when the water in the motor hits the maximum temperature of the thermostat. Then, let flow the hot water through the radiator and the cold water will flow back to the motor.
When you turn on the A/C, the motor works a little bit harder, that means that the temperature is going to increase, doing the cycle of the thermostat shorter.
EDIT Does not have to do with the A/C in the way that you explain.