Bob, I have talked to Pac Nor and Hart barrels. In fact, the guy that though of this whole idea of us using water down the barrel did R & D for Pac Nor. Steel has to get to 800* before it could ever be harmed by using water to cool it.
Bob, from start to finish, it takes 2 minutes or less to cool a barrel with water including patching out the barrel and drying the chamber.
I have my own private 300 yard rifle range with a shooting house that we shoot out of. I have a rack set up in front of the Air Conditioner that we put our rifes in front of to let the Cold Air blow across the barrels. It takes a while to cool even a sporter barrel, must less a big heavy Max Heavy Varmint contour that 1" at the muzzle or an unturned Blank.
Water is the fastest, easiest, and cheapest way to go, but the idea is so unconventional it is hard for folks to accept new things.