When engine temp gets high, the computer will turn off the Ac automatically until temp is back to normal. Sounds like a stuck thermostat or restriction in coolant flow since speeding up engine driven coolent pump helps with circulation (speeding up engine would not likely help if the problem were electrical). I would try a coolant flush and new thermostat. (Just an inexpensive and simple idea that might help.)
Note: If you can check the temp of the area around the coolant sensor, see if it is real warm. The sensor could be reading corrcectly and there is a build up of heat in the areas affected by the restriction. If you keep driving your car with this hot temp cycle each time it will not be long before the head gaskets will be leaking. This engine does not like overheating or hot spots.
