Herman, A # 4 stranded cable is rated at 70 amps and a # 2 is rated at 95 amps. Going to a 1/0 wire would raise the current-carrying ability to 125 amps. A current that is way beyond what the the circuits should need.
Beamer, could you post the size(s) of all the fuses in the primary 12 volt power panel in you Coach or just post the total current of all the fuses not including the main buss fuses.
Then post the main fuse size(s) if by chance there a 2 main fuses.
One could find a DC current prob at Lowes. They have them that can read 600 amps AC and 400 amps DC in the 40 to 50 dollar range if I remember. I have an Ideal # 61-768 and its been discontinued. Google it to see what it looks like !!
The closest one would be the 61-746 at $ 69.00 from Amazon. Could be $100 to $140 more at some outlets. Man things have gone up since I got mine.
Well , That might not be an option for you. Should you fined someone that has this type of meter, they can read the current flowing in the circuit. The total current draw through the Solenoid / Relay could lead you to an issue in a sub 12 volt power panel. Reading the voltage difference across the Solenoid / Relay.
Low resistance equals lower heat (low power loose). High resistance equals High Heat ( High power loose) Bad relay contacts. Time to replace the relay, but in your case you have replaced the relay. So that is not the issue unless you got a bad one and that could be determined by just reading the voltage on the input and output. Big difference, go back to the store, the one you got could be bad.
By chance could you attach a picture or 2 of the solenoid and the wiring around it ?
That much heat means a lot of power going somewhere, and the where is the real issue. The real interesting item is, being plugged into shore power; a charger is generally running at 30 to 40 amps.
Question, do you see any unsubstantial drop in the battery voltage level(s) ?