I can't see anything in this annual plot other than that the room temperature switches multiple times between -100 and 220 degC. I suspect you have too high a control action (otherwise you would not get such extreme room temperatures) and your gains are such that the control is unstable. At this experimental stage, I see no reason for adding an integral term in the controller as integral terms can cause instability if incorrectly tuned, and all they do is avoid a steady state error. Your first task should be to get a stable P controller with reasonable actuation power, and then if you need to reduce the steady-state error, add integral action.

This is the model i am working on! When i changed the parameters of the gain to 0.001 and Ti=300, then the model seems to work better. I also used the P-Controller as you suggested, and the results are similar to the PI case. For the P-Controller k=0.01. My question is if those numbers seem reasonable or are too small.