I have a Lennox electric furnace (heat pump w/ aux heat I believe) that's about 10 years old. The thermostat is a basic Honeywell digitial. The problem at hand is that the furnace only shuts off it you lower the temp setting 2-3 degree's below the room temp. It eventually kicks back on though and continues running until you repeat the process again of turning lower the temp setting. Plain and simple, it just keeps running and well after the room temperature is what we've set it for. (Ex. I set it to 68. It reaches 68 and then just keeps running.) Would replacing the thermostat with a newer one fix the problem or is it something more complex than that?