I have a 3 year old furnace that for the last 3 weeks has been acting strangely. When I get up in the morning and turn the heat up it fires up fine and blows hot air. But, after approx. 30 min of blowing hot air and BEFORE it reaches the set temp it cuts off for a minute or two and then fires backup. It seems to repeat this cycle quite often until it reaches the set temp. The air is always hot but it just stops for a minute here and there. I do not have a variable/programable thermostat. I changed the batteries and reset it but the issue continues. Next step, I guess, is to replace the thermostat...right? Anyone have any suggestions?