George;

Intermittents like this can sure make one crazy...having read your description of what happens twice, trying to understand it, I would think that it is more likely that alt output is being shorted (not the other way around, because a short in the alt drawing a bunch of bat current would indeed would fuse open the 8-10ga wire within about 10 seconds, and probably not go away afterwards...)...however a short within the solenoid as other poster suggested might cause this (shorts alt output, and also bat, so bat wire would get toasty too...)...in any case, I suggest putting a fusible link in line with the alt output wire to limit the current to something less than would fry the wire...also a temporary AMPmeter hooked up in a non-standard configuration in line with the alt would allow you to tell if it is a load on alt or within it!

Remember also that either the alt or the bat are supplying this power...for alt to supply power it must be turning...so does high load persist after engine is shut down?...bat can supply power any time, obviously...to put it in simplest terms: One end of melting wire must be supply, other end load...and the load drawing such heavy power is likely to be getting pretty toasty itself...so look for the hot device...

Keep a fire extinguisher handy just in case...

Good Hunting!