I would try bench testing the fan motor. Like convert says, that resistor is only there to lower the speed of the motor when you select "low" so if the fan does it regardless of speed setting (I'm unclear if thats what you mean) the brushes could be worn or the armature might be shot. While it's out, may as well throw a known good one in there and see how it does... problem persists, I'd check your power feed, maybe a corroded terminal in the bulkhead?
If you really want to get carried away, you could shoehorn in a heater case out of a mark IV lincoln, theyre thermostatic and everything's automatic
