I have a lennox furnace. At night I turn it down to around 55-60 so unless it gets really cold overnight it doesn't come on. In the morning I put it back to 68. A couple of weeks ago It stopped wanting to come back on in the morning. I tried a few things and what makes it light up again is running the big fan for a couple minutes. After about 3-5 minutes of the fan running by itself the furnace will kick on automatically and work like normal. Any ideas as to why this is happening?
Next you could have a motor or motor capacitor that is going bad. During the time the furnace is on the motor stays warm and wont seize. Turn the furnace on after a long off period it won't start on the low speed. When you turn the fan to "on" the blower starts and cooll the sfety limit and the burners light.
The capacitor is also suspect.
Been on many calls where the heat doesn't work after a night set back and cleaning a dirty flame sensor takes care of the issue. If they're right on the edge of working or not the cold will push it on the not working side. Worth a shot at least.