How long have you had the radio in the car?
did it start as soon as you installed, or something new??
Do you just have a radio, or do you have subs etc etc in there??
rust acts as a capacitor and so will drop ALL of your voltage aross that junction, but not allow any current flow across the junction. So your wiring is getting hot in areas that it should not, due to current flow trying to get to the other side of that "capacitor" rust. As the engine revs the ignition requires more juuce to run the car, and the alternator, not like people believe, it only outputs 14V's dc at 60 amps, whether your driving 3500 rpm, or idling, but the draw from it increases. I am not sure what kind of stereo you have, but surely check the grounds. Everywhere, especially in the ignition system, and the radio circuits. If you have a whompa thompa go to an increased amp alt., and maybe a dual battery. Does not need to be the super wango dango's from the car places, just another source for the radio to draw from. If that is where you are with the radio..