In most situations and simple control loops, P&I control is enough. What type of heater is it? How is heat applied and controlled? Where are your sensors mounted in relation to your heater? It sounds like your sensor has considerable amount of lag before you see a change in PV. All those are consideration of how much P and I you need. Try to measure a manual step response change. With a stable temperature, set manual heating output value, measure the time before you see a change in temperature. Keep an eye of the temperature and see if it stablelise (or close to limits), then turn off heat control. how long does it take to settle down again or does it keep rising?