I have 2 AK-47's and what I do is load a 10 round magazine, then carefully fire 1-2 rounds, let the butt of the rifle sit against my shoulder while still mounted on my front rifle rest, then check with my binoculars the effect of the two shots at 50-100 yards. This technique allows me to really monitor each shot, and the barrels stay cool.
The Ak design cools down the fastest out of any centerfire rifle I have shot, as they don't have a scope it causes me to check my shots and hesitate after using the binoculars. Both of these rifles are accurate, the Russian Saiga rivals several of my bolt actions in accuracy.
For some weird reason my Swedish Mauser Model 96 would heat up quickly, and would stay hot for quite awhile. This is one of the reasons I got rid of it. The last time I shot it I would fire 5-10 rounds of factory loads, and the barrel would stay very warm for up to 15 minutes, I have heard the Swede 6.5 has a high coefficience, so that may explain the heating problem. It got so hot that the wooded hand guard actually was painful to touch due to the heat, you can imagine what the barrel inside the wooden area was experiencing. If Sweden had gone to war in the Summer time I think they would have had a disaster on their hands with the scorchingly hot barrels. My Mauser 98's get hot, but not nearly like the Swede guns.