I'm not sure if the volt regulator is part of the alternator or not. It's common to combine them. The terminal is hot to the touch probably because the alternator is putting out too much voltage, or its spiking occasionally. I would put a voltmeter on the back of the alternator and see what readings you get, maybe put some accessories on, load the system a bit.

Overloading the battery is not a good idea (of course) so this may shorten the battery life. Heat is worse for batteries than the cold, within reasonable limits. I would get this addressed soon as electronic systems don't like voltage spikes, and this could get worse, or leave you stranded. Have any fuses blown yet?

I suspect that the alternator (by Bosch I think) has a built in regulator. With the drive to reduce parts, this a common setup.

Have you checked the battery connections (ground) to be sure they are tight and clean? It's sometimes the cause of electrical problems, and costs nothing to check. You should not need a new alternator/regulator yet. My 95 850 has 180K miles on the original alternator.