A dimmer cannot respond to temperature change. A thermostat can. Why are you trying to cut the thermostat out of the equation? Let it do its job. What happens when the temperature in the room drops? If you are using a dimmer the thermostat won't be able to run more to keep the cage at the correct temperature.
I still fail to see a point to what you are describing.Sorry, I'm trying to incorporate this method because I'm using a traditional thermostat (on/off) not a proportional like previous stated. Sorry for the confusion