Lot of people over think or worry too much about barrel heat.
According to Hatcher's Book of the Garand, it takes very little shooting for the M1 to raise temps to 500 degrees.
You'll get a lot hotter then that shooting the Infantry Trophy Match (where you fire as many as you can in 50 seconds, then move to another yard line and do it all over again. You do that at 600, 500, 300 and 200 yards>
Suckers get hot.
I measured the chamber of my Model 70, it went from 85 degrees before firing to 104 degrees with 5 rounds in no time at all.
Sounds bad, but it can't be helped. Any metal is gonna get hot when you add that much heat, energy and friction.
But it doesn't really hurt anything as long as the barrel doesn't make contact anything to disrupt the harmonics.
A barrel when fired is like a water hose, Un confined it wobbles all over the place in a constant patterned. No if you interject something to hit the water hose you're going to change the flow.
I've played with getting barrels as hot as I could, and different heat of ammo, like laying ammo in the sun vs. laying it in the shade.
Ammo is much more critical then the temp of the barrel.
I've shot M16 barrels and M-60 barrels until they got red hot. Once cooled they can shoot again.
Of course, heat will decrease barrel life.