When it comes to your heating system, the “brains behind the operation” is the thermostat. This component enables you to choose when the heater turns on, and what temperature your home will be. In some ways, it doesn’t interact with your furnace at all. Meaning, the individual components that make up your furnace will function as they’re supposed to regardless of what the thermostat does.
However, if something goes wrong with your thermostat, then you won’t be able to control when your furnace operates. Faulty thermostats can be pretty problematic, even when temperatures aren’t frigid. Imagine what a malfunctioning thermostat would cost you in the middle of the coldest day of the year.