Why does my gas furnace heat up and then blow cold air?
Sound like this may be the same problem as described on Why does my furnace need frequent power resets?

You didn't mention if the furnace comes back on on its own or not. If it doesn't (or doesn't as often as it should), it sounds like the exact same problem I posted about in the above link: a dirty flame sensor. If this is the case, cleaning it will probably make the problem go away.

If the furnace is coming back on on its own, then:


dirty air filter
Chimney is clogged causing exhaust to come back down the chimney (backflow)
Backflow sensor is clogged/broken
Flame sensor is dirty/broken
Control board is faulty


Checking the sensors is probably easiest.