After reading the Badger link, it is obvious Badger is talking about breaking in the barrel on modern high power rifles.
IMO, he has a point if talking only about these guns as they can generate a tremendous amount of heat if you rapidly crank 5 or 6 shots thru them. Remember, these guns usually have pressures in the 40,000-65,000 PSI range.
I don't think this really applies to muzzleloading rifles as the 20-50 seconds one usually takes to reload allows the barrel to cool.
The pressures in a muzzleloader seldom approach 20,000 PSI so the heat generated is much less too.
Maybe I'm slow during reloading, but even in Arizona temperatures I can't think of a time shooting my rifles has heated the barrel enough to even be concerned with.