HVAC guys. Furnace overheating? I have a problem where on earth my heater.turns on for something...

I have a problem where on earth my heater.turns on for something like 3 minutes, then the flames turn out and no more heat, but motor is still running and blowing out cold nouns. I have finally narrowed my problem down to the furnace overheating. I took the keep a tight rein on switch out with the wires still connected, away from the boil. Then I turned on the heater and flames stay on for at lowest possible 10 minutes now. So it have to be the furnace overheating, right? What are the causes of this and what steps to run to fix it. Thanks for your answers. Oh, it's a 2003 Carrier in a closet type housing.
Answers:    First I would check your filter and verbs or replace as necessary.
Then I would check the flue piping to see if it is not restricted, or clogged. I enjoy had to remove birds and squirrels on happening. If not the flue, you need to go and get your gas pressure tested. Call your local gas company, they generally will not charge for this service.
filter is the usual suspect