Last year I got a bit of a hot electrical smell then lost 1st and 2nd speeds, on investigation a couple of the wires going to the switch (just at the terminal ends) had slightly melted. I cut and soldered on new terminals and fitted a new switch.....

My thoughts are:
The blower is perhaps partially seized and so the extra load is drawing higher current so creating heat in the wiring.
MORE LIKELY THOUGH.....as it only happens when used on 1st/2nd speeds..the step down RESISTOR is getting hot because of this extra load from a partially seized motor!
So...where is the resistor? do you think it needs replacing at the same time as a new motor OR do you think once the new motor in replaced the load will drop and thus the resistor won't overheat.
Just preparing myself for what parts to buy.
Martin