Well, lol, don't get all caught up in the tacticool thing. 90 percent of the accessory stuff you see is just looks for the weekend ninjas. Some folks like a ghost ring aperture sight for range work and deer hunting and I'm one of 'em, but on a bird gun it'd get in the way. Wing shooting, you don't AIM the gun, you point the gun and swing with the bird.
Barrel heat is really only a big problem in combat on automatic weapons. Don't worry if your shotgun barrel gets a little warm normal shooting. This is one of the reasons vent ribs are popular on shotguns now days and you see these HUGE vent ribs on some trap guns. The theory is it gets the sight plain away from the barrel which can get warm enough to give convection waves off the barrel if you're firing a lot. But, as a practical matter in the field, I've never seen a problem. Nobody I hunt with uses a combat shotgun. I've never actually had the urge to OWN a combat shotgun, maybe a coach gun (double barrel 18" cylinder bore), but I'd really prefer one with interchangeable chokes so I could use it for something afield. You really need a choked barrel for bird or running game with shot to get effective range. If your shotgun's bored cylinder, consider just buying a new shotgun to use afield, will cost you a lot less than dressing one up from one of those tacticool magazines.
I've seen these hunting shows on wing shooting in Argentina. They make it sound like you never stop firing. But, I reckon, if you can afford a trip to Argentina, you can afford to take along two Browning Citoris so you can let one rest while you heat up the other. LOL!