Numerous possiblities I'm afraid, they do include the heat exchanger, it sounds like an overheating fault if you get heating for 30 minutes before shutdown:
Pump running slowly/sticking
Flue obstructed (causing fps to shut down)
Condense obstructed
Flue overheat stat problematic (most likely caused by the above two)
Main heat exchanger collapsed (if the heat exchanger is ribbed and not smooth)
Carefree
November 2010