I never really used the minigun on my first playthrough after the Concord battle, but during that battle I just naturally stopped firing a few times to let the barrel cool down. It never occurred to me NOT to do that based on all my previous gaming experience.
But the other day I was flying in a vertibird just messing around with the minigun and I kept holding down the trigger, and holding it down, and holding it - until it was white-hot - with no discernable bad effect.
So those of you who use these guns regularly: Is the color change meaningful or just for show?