Dianavan - it sounds like you have your problem solved. Remember that a thermostat is basically an on-off switch. If you have a very simple thermostat, it may not use power at all (it just serves as a switch for the relay that turns the heater off and on). Simple thermostats turn on at a certain temperature, and turn off when a certain temperature is reached. Usually, the range is set at one or two degrees so it's not a constant on-off-on cycle.
-Joe Offer-