I have a house that was built in 2005 with a Lennox gas furnace. When the temp out side is cold, but above freezing, the furnace has no problem keeping the house warm and to the temperature the thermostat is set at. The problem is that when it gets really cold(usually 20's or below, especially at night) when the furnace has to work more to keep the house warm, it'll stop coming on and the temperature will drop, and the thermostat will even register that drop(showing the temp 65 degrees when it is set to 72), but still no heat turned on. Turning it off and back on will kick the furnace back on, but most of the time it only runs for a minute before stopping again(rarely it will stay on, but that's usually in the morning when it's been off for a long time).
At first I thought is was the thermostat since with had a similar problem at our old place with the A/C that required a new thermostat, but I replaced it and it still doesn't work.
Any ideas of the problem and how to fix it? Is this something I would be able to fix?