The thing with leds.is that you may have to add resistors external or get canbus leds for the bulbs to work in a filament circuit and these resistors generate a fair bit of heat.
Hi power leds also are supposed run quite hot,but cos of led design the heat is generated internally or back thru the body of the bulb..hence the reason..at least on mine ,if you have leds fitted alone the lenses tend to cloud up more cos there is no bulb heat to clear the moisture..
However the op doesnt say its leds.
It sounds a bit general.but if connectors are melted check the wire tracks inside the bulb clusters to make sure there is no damp/rust/water bridging the connections.
(or the return wires connected to the bodywork as above)
Try and get the units you have as clean as possible,even if they have to be replaced later cos of the melting.
Leave them off the car ,just connected by the wiring and test and see if all the problems listed above are gone.
If they are it may have been shorting in the clusters.
If they arent .it could be switches..damp getting in further forward in the wiring loom..or other things