Jack,

I am assuming the alternator you are talking about is the big one.

It is cooled via an oil bath. The rear of it, as seen from the RH side door is actually an oil chamber that bathes the diodes. If you suspect it is shutting down due to heat(?) the oil supply line can be removed and you can check the flow by starting the engine. Do a rear start and rig up a way to catch the oil. If you suspect the alternator will have a high output in amps when you run this test, remove the field wire so it does not try to charge with no oil cooling. Any output in excess of 100 amps without oil cooling will damage the diodes.

The return line is the big line coming out the center bottom of the alternator.

The only way I can imagine heat being an issue, assuming the oil supply is adequate (there is a spec that I think I can find if needed) is if the alternator is really working hard, such as to charge dead batteries, or if you are pulling heavy loads off the inverters.

As to the regulator, I can't figure how it would get hot. All it does is sense the battery voltage, and open or close the circuit supplying 24V to the alternator field. The regulator is in the simplest of terms a switch that opens when the voltage reaches a specific point, like 28 volts, and then closes when the voltage drops below that voltage. All that switch is doing is limiting the voltage output of the alternator by removing power to the field. If it did not do that the alternator output voltage would go far beyond 28 volts.