I've got an Amish Country Spa that's run mostly non-stop for over 10 years.
Last week I found it cold, and traced it to melted wires on a 4-wire connector in the control unit. (They happen to go to the heater element)

I've read messages about connections going bad over time causing problems like this and only require cleanly replacing the affected wiring, but am not very confident this is the case here.
Any advice for how to proceed would be appreciated.

Yes that is correct.

That plug is for conversion between 115 and 230 volt operation. I hate these things.

I'd carefully mark and remove those wires, cut them back and make direct connections. Be sure that you've got good, clean, unoxidized wire when you make the connections again.

Regarding oxidized wires, I do still wonder why spa manufacturers don't use the anti corrosion gel that electricians use on connections inside household disconnects... only makes sense!

As other have said, just snip that plug (both male and female) and wire directly- be sure you're using good copper though- might have to replace some wire as well

Thanks to the great advice, the water is hot once again.
I greatly appreciate the help.