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Yesterday I put about 70 rounds through my Tikka T3 Lite in .223, 3-5 at a stretch. Temperatures were in the low 60s. After 5 rounds the barrel was just short of uncomfortably warm. These rounds use 26 grains of powder, or around half the charge of a .270 round. I'd wait 5 minutes for the barrel to cool off and then fire another group. There was a breeze and that helped cool things down faster. In order to help sped cooling, I'd prop my rifle on the shady side of the trees behind the tables, bolt open and barrel pointed up (nothing in the chamber and magazine removed for safety).
When I shoot squirrels, the temperatures are cooler and if the barrel hasn't cooled by the time I've reloaded the 5 round magazine, I'll shoot another rifle.
Yesterday three guys shooting next to me to check the sighting on their rifles would shoot one round, wait a couple of minutes and then shoot again.
Just a couple of reference points for you to consider.
