I am not sure that having power input as a factor is the right thing here. Power input is not something that you can set for thermal heating, is it?
If the temperature set point is the thing that you can control (even if that is not the actual temperature), then it makes sense to have that as the factor.
I would imagine that the set point and actual temperature will be closer in the case of thermal, but they would still not be exactly the same.
Ultimately, would it be useful to have a model of how your response(s) change as a function of set temperature?
You should make sure to add the interaction of Heating_Type*Set_Temperature as you could expect the effect of set temperature to be different for the 2 heating types.