your furnace is 120 volts. Inside the furnace is a transformer reducing said voltage to 24 volts. This is the control circuit. The thermostat is a 24 Volt application in your case. Not all the time. There are 120 Volt stats. But your is a 24 Volt appearantly.
So yes, the stat would be 24 volts. The furnace is 120 and your Air Conditioner is most likely 240. Have we completely confused you yet?
I fully support the military and the War on Terrorism.
If you don't know, then don't do. If you don't know and still do, then be prepared to pay someone else a lot to undo what you did and then do it right.
If you do know, then do. But do it right. Otherwise, you may not be doing it long.