I made a slip on coozie out of an old foam yoga mat. Its rare that my temp drops enough that I need to hit the fire, but if I do I just remove the insulator and flame on. Mine isn't rims, its direct fire.
I suppose I used the RIMS acronym incorrectly... My mash tun is also direct fired. I just use a pump to recirculate during the mash, but it does have a PID controller that kicks the flame on automagically when the temp drops.
So ideally I'd like a material that I can leave on the whole time (and won't burst into flames...).