For a room heater, PID does not make sense. It is very, very difficult to assure that a room is at a uniform temperature as proper mixing is almost impossible, without a lot of unpleasant air motion.
If the room is at significantly higher temperature than the surroundings, the doors, windows, walls, floor and ceiling will always be at lower and usually different temperatures (especially from each other), leading to convection flows.
Furthermore, if you have only one temperature sensor, it does not measure the "room temperature", only the temperature of its immediate vicinity.