I always just let them cool on the gun. Lock the bolt open and the heat from the can will cause a wicking effect and draw cool air from the bolt down the barrel and into the can until the can reaches ambient air temps. I've never had to dump and run with a suppressor so haven't had the need for it. I would guess you need similar material to actually put the suppressor back in a bag to carry it out, but I'd be hesitant to put a 500 degree suppressor down in a bag with ammo, mags, other guns, basically anything that could be harmed by the heat.