it could be a faulty T-stat,(seldom) but there are other things to check out first.
First of all, are you sure the actuall requested temperarure setting is being reached?or is it shutting down on high limit? When did it start doing this? is the air filter clean?
Take a probe thermometer and take a reading at the main duct near the SUPPLY plenum. Then take a reading at the RETURN AIR entry to the blower. The temp difference is the "heat rise". Compare it to the suggested 'heat rise' specified on the furnace label name plate.
Example; supply air reading=135
return air reading = 69
heat rise is 66
A heat rise more than what the furnace name plate is the reason for the high limit shutting it down.
Post back with some info and I or others will try and help.