Optimum Control Baseboard Heater

After taking a linear systems and control class I wanted to test out some of the knowledge by building a thermal model of my apartment and using some temperature sensors and some data from the local weather to try and regulate my apartment with the input being the angular displacement of the servo (not shown here as this is continuously rotating) and the output being the temperature of the surrounding air. Unfortunately the model was crap, the baseboard heater was highly nonlinear, and I found out a PD controller was much simpler. Regardless it was a good exercise in futility!