rule of thumb many folks like is if you place the back of your hand on the bbl and it feel HOT, its a hot barrel
BUT every gun will loose accuracy at its own temp/rate
I have a very accurate custom made light weight rifle, a thin bbl
after say 7-8 shots it will go from a 1/2 inch group, to a 3-5 inch group if I keep going
heat has a way of effecting all things, NOT just barrel, all metal when hot changes, most tends to get softer, and small changes can change many things from stiffness, vibrations, amount of flex,and so on
PLUS a hot barrel will loose rifling a LOT faster than a cold barrel or a warm one
yrs back when I used to take part in extreme testing of things, we used to shoot barrels to see how many rounds a barrel can take, from full autos to semi, or even a few bolt /pump guns(never tested a lever gun ?? don't know why)
but we have shot the rifleing out of many many barrels in less time than you think, more so on full auto's
and we have shot full auto's till the barrels melted and shot off the ends(don't recommend anyone do this)
hand guns have seem to be the best for NOT having heat related issue's, on most hanguns
super tight actions, and or all metal guns, can get hot to the point you won't shoot them without gloves, and most maintained a decent group, without a lot of growing in size groups that is
but I doubt very many folks want to take a sub 1 inch group pistol out and bang a few thousand rounds in a row out of it, or even a few hundred
without cleaning or taking a break
the amount of mags and loaders iof them and the costs seem to stop most folks if no other reason LOl