Ben instead of using a motor etc to control the temp. Try using a temp sensor and have the relay close the connection making the furnace or AC come on. Since the thermostat uses a coil with mercury to close the connection. You could have it done electrically. So it might take 2 relays since there are two connections that need to be closed. Fan and Cooling System. Here is a wire diagram: http://www.electrical-online.com/wp-content/uploads/2011/04/Thermostat-heat-cool-fan-on.jpg
