Back aorund the time Mastodon went on the Endangered List, I shot a fair amount of 3 gun. This was in a LE only league, where stuff was limited to agency/dept issue or its civilian equivalent.
I ran both issue 870s and my own. Some competitions had us running 60 rounds of buck and 10 slugs in short time frames.
At no time did I burn my fingers, and most of the drills were done sans gloves.
If you think a heat shield helps, fine with me. Mine won't have them.