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Replacing the speed control was a good choice. They do absorb power, especially when used at low settings, get hot (which is normal), and eventually burn out. It is an escalating phenomenon... as they begin to get hotter the lifespan of the switch drops quickly.
Since you did not notice any heat damage to the insulation on the wires, I think that you have completed the correct repair, based on the info you gave me.
Just a note: Dimmer controls for light fixtures work on the same principle and also eventually fail for the same reason... the long-term effects of heat buildup.