Thermostats are more problematic than they used to be now that they all have a computer board in them. If you suspect your thermostat is causing problems you can do a few things before calling for service or replacing the thermostat. Always change your batteries at least once a year. If you pull the thermostat off the sub-base you will always see at least 2 wires connected to it either on the sub-base or the thermostat itself. The red wire is carrying 24 volt power. This red wire sits waiting for you to turn the heat on. When you turn the thermostat to heat and and turn the desired temperature above the room temperature the furnace should run contiuously until the set point of the thermostat is reached. If the heat does not come on you can bypass the thermostat to see if it is the problem. So with the thermostat off the sub-base jump the red wire or the R termial to the W terminal or white wire. When you jump these two wires you are doing manually what the thermostat does when you initiate a call for heat. This could also be done at the low volatage terminal strip inside the furnace. Somewhere in the furnace you will see the R-W-G-Y termimals usually on the circuit board on a newer furnace. So knowing that the R or Red wire carries 24 volts and that the thermostat is nothing more than a switch that sends the red wire to the W wire on a call for heat we can easily diagnose if the thermostat is our problem.
G turns the fan on. So when you turn your thermostat's fan setting from Auto to On the thermostat connects the R to the G.
I am sure some of you don't have to read any farther to figure out what the Y terminal is for. Yes, on an air conditioning call the the thermostat sends or connects the R to Y. So on a cooling call that R or 24 volt power is sent from the furnace control board up to the thermostat, back down the Y or yellow wire and out to the air conditioner's contactor. Always when there is a Y call the thermostat will send power to G as well. Your air conditioner will not work without the furnace fan.
Sometimes you will see a 5th wire hooked to a B or C. Be sure you know what this is before messing around with it. A common wire is sometimes used when the thermostat is powered by the home electric instead of batteries. If the C wire is connected wrong it will burn out a fuse on the control board of the furnace or burn out a transformer on the furnace if no fuse is in the circuit.
Then more wires could be at the thermostat if you have 2 stage heating or cooling. They would be Y2 or W2.
This should help you hands on people with diagnotics.