Yep, definitely AC thermostat control. The thermostat has a capillary tube that is positioned
either inside the evaporator coil or in front of it. Once the set temperature is reached the thermostat
cuts power to the AC pump until the temperature rises again and reactivates the pump.
If your AC isn't working, check fuses to internal blower fan. Generally accessory power is taken from
low fan speed to activate the AC system. Power is then routed through the thermostat which is what
activates/de-activates the AC pump clutch.
If you have 12V inside the car, check that the AC pump clutch wire has 12V when the AC is running.
If no, then check to see if the filter drier(black canister normally, new ones are raw aluminium), about 8" long and about 3" in diameter
with a little sight glass in the top of it, has a pressure switch in it. If yes, then you may have low/no gas,
in which case the clutch on the pump will not activate - to protect the pump.
If no, you don't have a low pressure switch in the system, then still check for 12V to the pump. If you have 12V to the pump
and it still doesn't work, then either the field coil( this is what energises and pulls the clutch in) or the pump are FUBAR!