Do you actually practice using your Shotgun? Some just stow it under their bed in case of emergency, or don't really have a place to practice freely, I understand that.. But if you actually use it, to become proficient, then you will find the heat shield works as intended..
A shotgun practice session for me is at least 100rds of full power ammo.. With buddies, add more. Multiple targets and reloads, fired in multiple shot strings, 100rds will get the barrel hot enough for a shield! I have burned my hand on a shotgun barrel more than once!
With a tube mag pump, and the shoot 4 load 4 drill, loading on the fly takes some practice. Not easy to do smoothly, a hot barrel can make it more entertaining.. 
But, it makes it more challenging and fun that way.. 
I suppose that I've burned through more than 500 rounds of high brass ammo just this year. Typically 00 buck, slugs, #4 field loads and specialty self defense stuff like Winchester PDX. I've also shot hundreds of low brass as well. In 2010, I took a 2-day combat shotgun course. It was this class that showed me that traditional training courses were not up to the task of training for fighting in one's home. These courses focused on things that really don't matter when it's 3 AM, you're shaking off sleep, in your skivvies, trying to determine what you are dealing with in a darkened house... This class concentrated on basic skills, with debatable techniques. Old school stance, new school, squared-up stance, combat reload methods (most poorly thought out), and zero training on real world, home defense tactics. In short, all this class served to teach me was the general weakness of the prevalent training methods repeated by almost every trainer, everywhere. There are exceptions... I suggest googling Clint Smith and Thunder Ranch. Also, I recommend Paul Harrell's videos on YouTube.
What are the chances of the average person having to deal with a home invasion, burglar or other intruder in their homes? Pretty slim... But, what if it does happen? Are you really prepared?
The range is the proper place to learn how to manipulate the shotgun and pattern it with varying ammunition. One can practice techniques for combat reloads, magazine reloads and the like. However, the range is not you home's hallway. Everything you do at the range should already have been perfected in the home running drills with snap caps, in the dark. At the range, you learn how to shoot accurately with live ammo. In-home training is what will save your life. Train as you plan to fight and should everything go to hell, you'll fight the way you trained.
First, have a home security plan. This includes the most important factor... Keeping bad guys out. Proper locks, motion sensing lights, digital cameras, alarm system, etc. Inside, determine where you should defend if the need arises. Spouses and kids need to understand what to do. Practice drills are very useful. I have a buddy who sometimes sets an alarm clock for a weekend night surprise drill. Know how to clear a house, just in case you must get to a kid during an intruder situation. Have a fall back position with spare ammo stored there.
Proper defense firearms... There are many options. Pistols, rifles and shotguns. Opinions abound. Generally, I view pistols/revolvers as what I would use until I can get to a better weapon. I keep a loaded S&W 586 in the night stand drawer. I keep a loaded 12 gauge pump shotgun in my bedroom closet. We have no children in the house. My grand kids live in a different state. When we have visitors with kids, we lock up the hardware. My combat shotguns are all set-up the same basic way. Sling, side saddle and improved sights. Two have LED lights, although my home can be lit up from a master light panel in the master bedroom (every major room/hallway has an LED high hat in the ceiling wired to that panel, which was installed because my wife is disabled and she can illuminate rooms before she leaves the bedroom. She suffered a trip and fall injury in the dark, so I had the lights installed). I could write an essay on how to "harden" your home to intruders. Obviously, the best home defense is keeping bad guys outside....
I won't shoot in the dark. One shotgun has a reflex optic, and all have fiber optic sights. Any other hardware installed on a shotgun is extra weight and generally of no tactical value. I load Winchester PDX-1 buck over slug ammo in the magazine and side saddle, except that I keep two rifled slugs should a more precise round be needed. There's spare ammo in several out of sight locations. A 9mm carbine is also stored in the closet, with two magazines loaded with 115 grain JHP ammo. Everything else is in one my two gun safes.
The thing about that heat shield... It is helpful on the range. Like you, I've burned my hands on a hot barrel several times (which is why I often wear gloves). In a home defense situation, if I've fired often enough and fast enough to get the barrel hot enough to burn me... I'm probably in a war rather than a home defense fight.
Less than five rounds should decide a home defense situation. Although, I'm prepared if that isn't the case.
