What could cause a melting/overheating light switch?
It sound like you have a partial ground from a pinched or nicked wire. This would draw a large amount of current but not enough to trip the breaker.

If the switch is overheating I would suspect the partial ground is in the load side of the circuit after the switch.

Check the circuit with an ammeter to determine the current draw. If you don't have one remove all your lamps from he light fixtures and see if it still gets hot. You could also series a lampholder with an incandescent bulb to the switch with all othe lamps removed. If the lamp lights up you have current flowing to a partial ground.

Good luck!