A broken or inefficient thermostat can lead to uncomfortable heating problems, making it seem like an issue with the furnace. However, thermostats should be the first HVAC components to check during furnace trouble.
With a faulty thermostat:
The furnace will not turn on.
It will display the wrong temperature readings.
The furnace will heat a home unevenly.
The thermostat won't respond.
The furnace will consume more energy--higher energy bills.