Taking 2 or more rifles and alternating might be your best bet, Jon.
When I go to the range, my typical procedure is to set up a large target with several bullseyes on it (home made), take several rifles, and test several rifle/load combos alternately. Like, fire a 5 shot group from one rifle, examine the group thru the spotting scope, record velocity, etc, on a sheet I keep next to me on the bench, then switch rifles.
Repeat
By switching rifles, after 5 or 10 shots, you keep the barrel from getting too hot. And by using a big target paper with several aiming points, no going back and forth after each group.
The one danger of my method of range shooting is that you may be using several different calibers of ammo on a given day. Make DARN sure you put the right ammo in the right rifle

. I make it a rule to only have one caliber of ammo on the bench top at a time- when I change rifles, I put the ammo I was using in my range box, and bring out the caliber for the rifle I will be using...and I check several times!
I have draped a wet towel over a hot barrel on hot summer days, when I only had 1 or 2 rifles to test, and not much time. I don't know if that really helped, but it made me think it did