Wouldn't work, there are multiple electric components that need constant power. Heating using a resistive element (like flexwatt/UTH's/Heat bulbs) is simple because all they do is turn electricity into heat. To cool something down is far more complex. There will at least be a compressor and possibly other electric components that certainly wouldn't be able to run off of a proportional thermostat. A on/off style thermostat might work better, but things like compressors usually need to run at times even when they are not actively cooling the unit. Compressors also generally have a duty cycle that prevents them from turning on or off at certain times and cutting or applying power could mess with these cycles.