A long 3-gun shotgun stage would be 35 or so rounds, as fast as they can be shot and reloaded. A home defense scenario with that many rounds is hard to imagine. If a HD shotgun has a heat shield, leave it. If it does not, not sure I would add one.
For example, my 1100 used in 3-gun does not have a heat shield, and I have burned my hand. Not badly, however not pleasant. The vent rib helps a little. My 590 has a heat shield, and I have used it in matches. It gets hot enough to burn.
The 60 degree F difference between summer and winter (for me) makes a big difference in "burnability". Oh, my AR barrel gets hot enough to burn as well, even the carbon fiber fore end has gotten toasty at 100 degree, high round count, matches.