The thermostat in your house tells the furnace when to switch on or off and, if you have a cooling system, controls that as well. When the furnace fails to switch on or off as it should, the problem may be with the furnace -- or it may be with the furnace's brain, the thermostat. You can test whether your thermostat is working or not and thus cut down on the time a repairman has to spend doing the same thing, with the help of a friend.
Replace the battery, if present, on your thermostat. A weak or incorrectly installed battery may make it appear as though the thermostat isn't working when, in fact, it is.
Check to see whether the furnace is running. If it's not running, set the thermostat to "Heat" and make sure the fan is set to either "Auto" or "On." Set the desired indoor temperature to at least 10 degrees above your heating set-point, if you have a programmable thermostat, or at least 10 degrees above the current temperature if your thermostat is not programmable. Listen to see whether the furnace comes on. If it does come on, your thermostat is working.
Try setting the thermostat to cool, if that setting is available, and if your furnace is already running. Set the temperature to at least 10 degrees below the cooling set-point if your thermostat is programmable or 10 degrees below the current temperature if it's not programmable. Listen to hear whether the furnace switches off or not. If it doesn't switch off, or if it didn't switch on when you tested the heat function, there may be a problem with your thermostat; you need to check one more thing.
Ask a friend to go stand near the furnace while you manipulate the thermostat.
Set the thermostat to heat, as before, and adjust the temperature setting up as before. Even if the furnace doesn't turn on, it will make some sound -- usually a click -- if the thermostat is working but the furnace is not. If you repeat this test several times and your friend standing near the furnace doesn't hear even the faintest click, the thermostat isn't working properly; its message for the furnace to turn on is never reaching the furnace.
Repeat the listening test for the cooling function on your furnace if the furnace is already running. Lower the temperature on the thermostat while your friend stands by the furnace and listens. It'll be harder, with the noise of the running furnace, but he should still able to hear a click if the thermostat is working. If he hears clicks but the furnace doesn't turn off, the problem is with the furnace. If he doesn't hear any clicking, the problem is with the thermostat.