Urgent! Fire! Help!

Does this car have an aftermarket "killer stereo" installed? When pulled into a parking space, does it trip the motion sensor alarm on nearby cars? It sounds like you have unusually high alternator current demand, or the lug-to-cable connection at the alternator is corroded and/or damaged.

That wire should run warm with high electrical loads, but if it is melting the hood liner, the wire insulation and electrical tape will likely be next. Hopefully, your Mustang has a fiberglass hood like mine does.

I would think about replacing the wire. It would be OK to rotate the lug to a move favorable angle if you remove the lug and fit a thin insulator under it. The insulator will prevent electrical contact between the lug and alternator housing. It has to withstand high temperature. A 1" x 1" piece of epoxy printed circuit board material with a hole drilled in it would be an example of an effective insulator.

Did you ever determine where the original short circuit was?
 
Does this car have an aftermarket "killer stereo" installed? When pulled into a parking space, does it trip the motion sensor alarm on nearby cars? It sounds like you have unusually high alternator current demand, or the lug-to-cable connection at the alternator is corroded and/or damaged.
No aftermarket electrical devices are installed. Stock 460 stereo, no extra lights or neons or anything like that.

That wire should run warm with high electrical loads, but if it is melting the hood liner, the wire insulation and electrical tape will likely be next. Hopefully, your Mustang has a fiberglass hood like mine does.
Stock hood/hood liner, I'll try to take some pictures of the hood liner itself tomorrow to help with the description here. It's possible that melting may be too aggressive of a term for whats actually happening.

I would think about replacing the wire. It would be OK to rotate the lug to a move favorable angle if you remove the lug and fit a thin insulator under it. The insulator will prevent electrical contact between the lug and alternator housing. It has to withstand high temperature. A 1" x 1" piece of epoxy printed circuit board material with a hole drilled in it would be an example of an effective insulator.

Did you ever determine where the original short circuit was?

I'll also get some pictures of how the lug is currently situated/the spacing between it and the alternator case so that I can get everyones opinion on that.

It's entirely possible I suppose that the wire is just running 'warm' as you say, rather than superheated and I may simply be over-reacting, I guess.

When using a multi-meter, the voltage at the battery with the car running no load and with load was approximately 14-15 volts, it is my understanding that that is within normal parameters, however I may be misunderstanding what you meant by 'high alternator current demand', as well.
 
It would be handy to know the current draw on the wire. A DC clamp on amp meter is really needed.

Are you sure it's not the alternator getting hot and transferring the heat to the wire?

I've got a multi-meter with all sorts of functions on it, would that be adequate to test the current draw on the wire?

As to the alternator transferring heat, the alternator was rather warm as well when the hood was popped, so that could also be a possibility.