Sounds like it might be the wire to the ammeter. You should probably replace the alternator too.
Which one is melted? Could be a starter solenoid, ignition or ammeter wire; the latter only if your car had an ammeter.Was looking over things and there is one wire on the harness under the hood that runs from the starter solonoid, that is bare ( split open/melted) all the way from there to the plug at the firewall.