Grounding could be a problem that might cause heat buildup. When the ground is nominal, the system "SEARCHES" for better ground and heat develops. In the case of a generator, this can be nothing more than too much paint on the mounting brackets or the mounting boss where the generator mounts on the front timing cover. When I rebuild a generator, I'm extra fussy about the ground between the front and rear plates and the generator case and even between the rear mounting bracket and the case. Assuming that all of those places were blasted in your rebuild, those areas should be OK. When you get the replacement, sand the paint off the mounting points to bear metal. If you're concerned about rust developing, a very light (VERY LIGHT) coat of grease won't hurt.
As per the charging rate, unless you plan lots of night driving, 6-8 amps at high RPM should be plenty and should stop any other overheating scenario in the generator itself. Of course, we also need to assume the rest of the wiring, electrical contacts, battery cables, and battery itself are up to snuff. If you've purchased a rebuilt generator to solve other electrical issues, you're working backward.
Good luck.