I have two wraps but really only use them to mitigate mirage for precision shooting. Otherwise my suppressors are bare and I use gloves to handle them.
What I am wondering is, if you shoot enough to create suppressor mirage isn't that enough to create enough heat to be worrying about a wrapped suppressor?
"Never forget, even for an instant, that the one and only reason anybody has for taking your gun away is to make you weaker than he is, so he can do something to you that you wouldn't let him do if you were equipped to prevent it. This goes for burglars, muggers, and rapists, and even more so for policeman, bureaucrats, and politicians."
-Aaron Zelman and L. Neil Smith, Hope, 2001
I use the HAD wraps from riflesonly.com. Yes they mitigate heat, but more importantly keep me from scratching my suppressors running through the brush and mitigate mirage when when shooting long range. No, I don't do dumps with them on. I use them for hunting and bench rest shooting only.
It would be interesting to test long term, because my thinking from car days and wrapping headers. Holding in extra heat can stress the metal and cause premature wear and failure.
I also like the Rifles Only HAD, . I use mine when shooting long range to mitigate the mirage. They have a few options including a pouch made of heat material and a new protector which is the "skinny" it is only the outer. I would not use a cover if I was doing multiple mag dumps.
I don't use wraps on my issued M-4 or my personal carbines at all. The only reason I would consider it is if my clothing wouldn't protect me from the can during transition drills.