When you say not in use, do you mean when the motor isn't running? If that were the case, it would seem that the heat is from current draw and resistance. That would be drawing amps from your battery that can be measured. Do you have an amp gauge to measure the draw?
If you mean that it gets hot while running, but not putting out much current, that might be from excessive friction, which is usually a bearing. You could stop the motor, let it cool, then start it up and put your finger on the alternator to try and determine where it's getting hot first. Little laser thermometers are getting pretty reasonably priced now. You could point and shoot at your alternator to find the hot spot as well. Just some initial thoughts.
1- This could be a couple of things normally an internal short or a bad rectifier diode. A diode is a one way electrical check valve and if they fail they can sometimes allow current to flow the wrong way or backwards into the alt, not out of the alt. With the engine off the battery bank is trying to flow back through the alt and getting it hot and heating it like a heater...
2- The regulator could be wired wrong and is simply full fielding the alt if wired in an "always on" manner...
Disconnect the B+ output wire and see if the issue stops. If so bad ectifier or internal short.
Disconnect the field or regulator wires. If the heat stops it is in the regulator wiring..
Any alt shop can repair blown diodes. This most often occurs because someone passed through the OFF position of the battery switch with the motor running.