Have you verified for sure that the thermostat is the problem?
the furnace could be heard kicking on but nothing would come out of the vents... the control on the thermostat would jump from reading the room temp from 68 to 75 then back to 72 within seconds.. therefore we figured it was the thermostat..
Remove the thermostat cover. You should see a R terminal and a W terminal. Remove the wires from these two terminals and twist them together. If the heat comes on let me know.