replace both the positive and negative batt cables. make sure the neg cable is grounded good. I would then look into a 3G alt upgrade. these are far better alts and you can find a 130amp at a wrecking yard for cheap. then go to fordfuelinjection.com and pickup the wiring harness and fuseable link . this will complete the swap an probably take care of your issue.
i suspect that your alt has a built in regulator thats probably hosed, or the wiring is old causing to much resistance which then creates heat.