Sounds like the thermocupler, that's what tells the furnace when to light, etc...
I Have An Arcoaire RPJ II Furnace, When I Turn Thermostat To Heat, It Comes On Like It Should. Glow Plug Lights, Then Burners. After About 5 Min. Burners Go Out And Unit Cycles Glow Plug Back On But Burners Don't Light. I Have To Cool It Down First. What Could It Be?
Is it a direct vent furnace. If it is, maybe something is obstructing the flue. Check it out