I also clean my barrel and let it cool between every shot. It's time consuming, but I want to be sure that first bullet out of a clean cool barrel will go where I want it to. I'm not worried about how it groups 3 shots later out of a dirty hot barrel.
AMEN. How many times have we read a thread out on the board here like "loading problems", "crud ring buildup" or "why is 777 so hard to clean". Treat your gun to a patch between shots and you will recreate the hunting barrel you'll have out on opening morning. I don't take my gun to the range to rain down bullets as fast as possible just to get them all in while the firing line is active before everyone goes down to check the target. Our firing line is open for 15 minutes and I'll shoot 3 times only. In between shots I patch twice and reload and fire a 22 plinker for fun. My last shot is taken when the rangemaster calls for the final shot of a chambered round. That way my first shot is taken about 10 minutes later out of a cold barrel.