This is what my furnace does. While running and when the thermostate reaches the right temperature. I could hear it click back on and then off and then back on again. While it was in the cool down mode. The thermostate does reach the right temp. I could also see the flame light back up while all this is going on. There are no door open to let any cold air in to make the temperature drop that fast. It is a old furnace, it is a Sunbeam. Yes I know I should replace it. But it is still running.