The root cause of the problem is tight motor bearings from leaks through the pollen filter.
The normal reduction in speed is by heating up the resistors as voltage to the motor is dropped - it always takes the same current. If the motor/blower runs slowly, there is too little air going past the resistor pack to cool it, on the way to the heater box. So the thermal fuse gets too hot and does its thing.
Also, an electric motor that is not free running actually takes a higher current than it should, though not enough to blow the conventional fuse. The fan switch contacts seem a bit marginal as this higher current causes sufficient arcing to burn/melt the contacts.
Hope that makes sense.
Martin