My Nomad-LT always wears its cover, because, like was mentioned, it helps mitigate mirage, burning the shit out of your hands, burning up anything the can leans against or touches, shit melting to your can and then cooling and being permanently stuck to it, and even when it's warm you can still remove the suppressor and sit it on the bench to cool because the cover will keep the bench from melting.
Also, most .22's don't have enough powder to generate the heat a centerfire rifle does. I have gotten my Dead Air Mask HD pretty warm on my 5" Kimber with the .22LR conversion. That short of a barrel and rapid-firing about 40-50 rounds, there is a lot more heat than with a 16"+ rifle barrel. I have never gotten my can hot on my 10/22 or my CA Ranger 22 (bolt-action) with subsonic, and shooting fairly long strings. The can is typically barely above room temp, maybe ever-so-slightly on the warmer side, but you can still handle it, remove it, lay it on the bench, and it's more than cool enough to be safe. So, no, I don't use a cover for my .22 suppressor.
I saw some moron on IG earlier with a sub-comp Glock and he had a can on it, with a cover, and the whole thing was about 3x bigger diameter than his sight-picture... It was literally point and shoot, no chance of aiming at all. You really just can't fix stupid.