Forgot to mention, if you use a proportional controller for the heater, you can still use the fridge for cooling if it goes over temperature (provided you have a suitable cooling stat). I have tried deadband controllers, but it is very hard to size your cooling and heaters and position your probe suitably to get stable control (because of the lags in the heat/cooling being transferred to the air) unless you have a wide deadband on the temperature control.

Good luck,

Ed