Presumably the AC still has a thermostat. For this application it would be set to be much higher than the set point but it would effectively serve as the second

Presumably the AC still has a thermostat. For this application it would be set to be much higher than the set point but it would effectively serve as the second controller. Failing that, the worst that could happen is that the space would get cold. The compressor motor itself would be thermally protected.