I often shoot from my barn window. I have a deep freezer in my barn.
I don't usually even think about barrel heat, unless shooting muzzleloaders with sabots in summertime, when you have to keep the barrel cool or ruin the sabots.
I may or may not have been caught stuffing a muzzleloader into the deep freezer to cool it down during the summer.
As for hot barrels in general, here's the thing: I completely grasp the statistical value of 10+ round groups, but I also grasp that ammo costs money and a guy who's hunting almost 100% within 300 yards can live with a single click worth of statistical zero (or composite cone of fire) uncertainty. I'm not sure exactly where that single-click level of certainty is breached (I'm guessing 5-7 shots will usually get you within a single click of zero, I haven't ran the math and am not sure I could) but from a personal skill standpoint, on a budget (a whole, whole lot of the discussion on this forum seems to assume an unlimited supply of ammo, which I do not have - I can generally afford all the .22lr I can shoot but not all the centerfire ammo my kids could burn up), I generally don't put much value on high-volume practice precisely because I believe that building and locking in to a field position is the harder part of the shot. Once you have a solid position, certainly there's value in trigger repetition, but given a choice, if I had, say, 100 rounds to make someone a halfway competent shooter, I'd have them getting into position 50x and shooting 2 shots per position, instead of having them get into position 10x and shooting 10 shots per position. Put another way I believe there's a diminishing marginal value in subsequent shots once you've got into a position and the greatest value is had by practicing the position, not the trigger break. Or, maybe we should report how many times we built a position per range trip, not how many shots we fired. I mean, yeah, that turns into an aerobic exercise, and that means work and sweat. I get that. Shooting is supposed to be fun and what I'm proposing turns it into armed jumping jacks. I won't pretend to know what the optimum ratio of shots per position-build is, but I do believe it's way the heck less than 30.
YMMV. I'm not the expert here.