The thermostat instructs the heater on how to function. You set a temperature, the thermostat sends a signal, and the heater responds.
Of course, this also means that any issues with the thermostat could be causing the heater to malfunction. That issue could be anything from a programming error to a genuinely broken thermostat. The next time you believe that your heater is giving you problems, hold off on calling for furnace repair in Long Beach, CA.
The problem could simply be one of these thermostat issues: