The Car Show is a good outfit, so they will find the problem and correct it. In the meantime, let me comment that the #12 wire is more than sufficient to carry the current to the refrig, so I conclude that some other source of heat is discoloring the wire. Perhaps it is too near the chimney?
I'm not sure why the wire is white - I would have expected black - but my TM is closed up in the garage at the moment, so I can't offer anything constructive in that area.
By the way, some (but not all) tow vehicles do not provide sufficient electrical power to the TM to run the refrig while towing. My 2002 Explorer (which should be similar to your 2003 Expedition) was one of them. The Search tool should uncover my none-too-polite post on the topic, in about 2003.
The original post has apparently been lost, but here is a follow-up.
http://www.trailmanorowners.com/foru...ead.php?t=4909
Bill