My wife and I have an 1986 CC 38. Love the retro thing. Isn't the wood work just gorgeous? Take care of it and it will last. I would recommend you check the belt tension for your charging issue. And use the pound tension method, not your hand, a board or anything else. They make tools for it.
What engine do you have in your rig? For example I have the CAT 3208T 250 HP, which was the exact engine setup I wanted, but they phased out toward the end of the decade. Do you have the Detroit 6V92? They also made a 350HP version of the CAT. That tended to blow out the rings if you are not careful prior to a rebuild. CAT fixed the problem, but not on the first go around.
For CAT here is the belt tension check
CAT 3208 BELT NUMBERS and their PROPER ADJUSTMENT - Wanderlodge Owners Group
For the 6V92 I didn't find a quick applicable guide but you should be able to google your way into finding a process. Note: Some the Detroit engines have a valve controlled belt tensioner that gets stuck and causes overheating at high speeds.
If you have a different engine setup follow their procedure. Everyone has one. CC recommended on my coach that the alternator be rebuilt almost yearly, and I have the original manual that describes the process of how to...(so they were serious about it)...I am not certain it has to be that often, but we will see. It should produce 14 V. If you test it at the alternator and then check you batteries you can trace any drop off.
Also, do you use the six volt batteries, or did you convert to 12's for the house batteries? Neither is a problem, it's just the setup can influence the charging on the go-if your house batteries are not getting enough current.
What was your gauge reading for water temp, oil pressure, and oil temp when you became concerned? Do you have a AT temp gauge? I don't on my mine due to its age, which isn't a problem for me. Do you have a belt driven fan on your rig?
You need to watch for lugging if you are not used to these vehicles? If you are experienced with these rigs excuse the comment. That will heat up things rather quickly. Also, have you tested your coolant unless you have the ELC type?
After these checks overheating goes very diesel and weird for the average guy, but certainly fixable and fun to learn about.
Enjoy your coach. It's a looker.