LEDs can get hot, but it depends on how much current it is fed. My Luxeon K2-based license plate and parking light is fed around 114mA @ 3.5V, and it gets lukewarm at worse. The map light is 350mA, and it has a heat slug. The trunk light is around 600mA with a small heat sink attached to it. The turn signal bulbs are around 266mA, and it has a small heat sink as well.
The LEDs melting plastic can be caused by a short, being overdriven, and resistor burning up. It can also be caused by inadequate heat dissipation so heat has to go somewhere.
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