The best way to do this is to connect from the negative pole of the alternator (the one that is actually a stud in the alternator case) to the place where you ground the battery to the engine block. This merely makes sure that the alternator has a good ground to the block, rather than relying on the connection through the mounting hardware.
You do not want to go directly to the battery, because then you have added a wire in parallel with the heavy one that carries the start current, and if that heavy primary ground wire develops a bad connection, the start current will try to go through your alternator ground.
It is possible that the alternator is heating up because it is charging harder. You can check the voltage and see if it is putting out more. But, "charging harder" means putting out more current. This is hard to measure without special stuff. But if it is getting really hot, then it's something else.
I would check to be sure that the new wire is actually going to the alternator case. There are other studs on most alternators, but the ground one has of course no insulation from the case, it just sticks out of it. I would be sure to connect directly to the engine block, preferably where the ground wire from the battery connects, but any good spot will do. I would use 10 awg or even 8 awg wire, since the 10 is only rated for 50 amps or so, in case your wire ends up carrying all the charging current
If you can tell me what kind of alternator and regulator you have, I will look them up and see if there is anything unusual....
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida
