I have a very old furnace that heats up fine but the blower will not shut off. I called out a repair person about a year ago and he said that he has never seen a gas furnace as old as mine. He ruled out the thermostat, but did not give me any more info. He was too busy trying to sell me a new one, I am beyod broke at the moment and I need that furnace working. What else can it be?

A brand and model number would be nice so we know exactly what you are talking about but since you did not provide one I will guess and say it is a fan and limit control that got old and stuck in the on position OR on some of those controls there is a white button that got pushed in which will also lock the blower on.

could be a fuseable link on wire that connects to the limit switch