Most men can handle around 160-190F on there hands. I know I've had my shotgun out in a hot day and the barrel got damn close to burning hot. I wasn't stupid enough to see how hot it was later. Gloves help, but not always the first choice. Many rifles have something similar, full auto mostly. I've seen quite a few trench guns with heat shields and they weren't even used in the deserts. In the end, if you are wearing it on a sling and sling her up, or a single point and drop it, the chance of that barrel searing a soft spot is increased.
Those are my thoughts. Would I do it? Well, haven't done it yet and that's about the cheapest addition for a shotgun. I may do it, but if anything it'll be mostly for looks.
"Today is victory over yourself of yesterday; tomorrow is your victory over lesser men." - Miyamoto Musashi
[Insert random irrelevant religious quote here]