I took a break from working with a “big” microcontroller to work with a little one. The PIC12C671 is definitely little when compared with the PIC18F66K80 I am using in the GenPIC utility PCB. With less than 2k of program space and a mere 128 bytes of RAM it is definitely limited. Consider that the chip only has eight pins, two of which are power and ground, leaving six I/O pins to get the job done. No problem, I only need two I/O pins for this task and that few bytes of RAM is more than enough!
A bang-bang controller is inherently reliable and stable because it uses two different control setpoints, a high and a low. Because these control points are separated by a large margin, called hysteresis, the controller will not oscillate or rapidly turn on and off. In this case the heater will not turn on until the temperature falls below 10°C and will not turn back off until the temperature rises above 15°C. That five degree margin is called hysteresis, and ensures a good period of time between on and off.