It doesn't matter which method you use for temperature control and temperature reading. A thermal fuse should still be used with a wall plugged heater. You never know when your thermocouple slips of the heater and starts indicating room air temperature instead of heater temperature. This fools your PID controller that it still has not reached the target temperature and supplies current continuously to the heater. 120-150 degrees thermal fuses are cheap, you can even scrap them from certain household appliances (some baby bottle sterilizers have 130-140 degrees thermal fuses, for example).