I know my 30-06 with a standard barrel can only handle about 4-5 shots before getting too hot to hold with a bare hand. I wait about 8-10 minutes before shooting another group of 4-5.

I recently went to a precision rifle course where everyone would shoot a group and then walk the range to check targets (but really it was just built-in barrel cooling time). The instructors even told me and another guy shooting 300 Win Mag to only fire 3-round groups at certain points to help us keep the barrels cool. I had never realized before this course just how important barrel temp can be.