I don't understand why he can't just connect / disconnect the power? The thermostat is a bi-metallic strip.
Assuming the thermostat is controlling 120V AC:
1: There are plenty of cheap wireless thermostats for AC that you can buy off of Amazon. I have two, and they work great with space heaters.
2: You can use a 120V relay with those thermostats to control different voltages, amperages, ect.
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BTW, controlling the dial for min cool, max cool, ect, could increase efficiency. Max cool is only needed if the unit's been off, or it's a super-hot day.
Assuming the thermostat is controlling 120V AC:
1: There are plenty of cheap wireless thermostats for AC that you can buy off of Amazon. I have two, and they work great with space heaters.
2: You can use a 120V relay with those thermostats to control different voltages, amperages, ect.
---
BTW, controlling the dial for min cool, max cool, ect, could increase efficiency. Max cool is only needed if the unit's been off, or it's a super-hot day.