Thanks for the good advice Beretzs.

Part of it is I seem to get tighter groups with my .340 doing the way I did, but that also could be a coincidence.

Either way, I generally fire the first three shots of a range session in fairly quick succession, including today, which makes me think that, in the hunting scenarios, the rifle never will get hot, because those first three never seem to cause the barrel to get very warm. It's just that, after that, it seems to keep getting hotter and hotter if I don't leave some time between shots. I usually bring two rifles, so I can rotate. I think I'll do that next time, and do what you're saying, only maybe waiting ten minutes between each group while shooting something else and/or reading the 24HCF on my phone--to let the rifle cool between sets.

Unsurprisingly, the heavier barrel I have tends to heat up more slowly, but it also cools down more slowly.

Have a good weekend.