air conditioner only works part of the time

If this has an HVAC system when the outside temp drops to under 41 degrees the AC system is shut down by the computer, so if the temperature reading is 0 then the AC will not work.

Sounds like a problem with the coolant temperature sensor. Possibly a bad connection at the sensor. When the computer loses the signal from the coolant temperature sensor it assumes that the engine is overheating and takes steps to help prevent engine damage. One of those things is the air conditioning is disabled. The fact that the engine temperature gauge drops is also a good indicator that the coolant temperature sensor is the problem, or the wiring going to it. Hope that helps! Jim