I have an older Tempstar gas forced furnace. The cycle starts up fine and about 3 minutes into it the burners shut off but the blower keeps running. The burner shuts off after the switch makes the upper temp limit like it is supposed to. I have replace the rotary temp switch twice. After I change the switch it worked fine for the rest of the season but the next season it starts all over again. The rotary switch is a Honeywell.

What do you have the switch set at? Does the switch have 2 settings? You might have an air flow problem, pull the filter out and see if it does it again.