The nylon ones melt because I'm dumb and put my can in there hot. She's using nomex and insulbrite (the stuff used for making pot holders). It will also have paw patrol fabric on the outside because my son picked that out. Will report back if it catches on fire.

How should I test? I figured bust a few rounds, take a temp with an infrared and just keep going until I get to like 600f and see if it gets damaged? Anyone else ever tried this?

Are you going to do an inner sleeve too? If so, What is the material?

https://www.oatey.com/products/oatey-flame-protector--2068652191

Or similar. Rated for direct flame contact.

Oatey® 9 in. x 12 in. Bagged Flame Protector

Oatey® Flame Protector is a Zoltek Pyron® based heat shield designed to protect studs, walls, floors and other surfaces from sparks or flames. It can be used on lines carrying water, steam, caustics and dilute acids. Made with flame-retardant Zoltek Pyron fibers and ideal for use while soldering near studs, joists or walls. Oatey products have earned the trust of plumbing professionals for over 100 years.
UPC: 038753314006
Part #: 31400

Protects studs, walls, floors, other surfaces from sparks, flame
Can be used while soldering near studs, joists or walls
Ideal for use with propane and max power propylene gas torches
Made with flame-retardant Zoltek Pyron fibers
9 in. x 12 in. cloth
Withstands temperatures up to 2,500°F
Includes brass eyelets for hanging from a stud or wall

That's a good idea. We're thinking nomex for now as you can buy it by the yard relatively easily.

Nomex, so should be good to 600f or so. If you do more than one layer you can hit like 850f or so. I figured it would be fine for a shoot, let it cool for a minute, and throw it in a bag to make the trip home kinda thing.

I don't know s#!t about suppressors.  I used to tinker with cars, turbos, and high exhaust gas temperatures.  I don't know if it'll help but when it comes to controlling heat; DEI
https://www.designengineering.com/products/heat-control/?_bc_fsnf=1&Radiant%20Heat%20Resistance=2000%C2%B0F&sort=priceasc

A bucket of water will cool you down to 200 f real quick.

Is it safe to rapidly cool down suppressors like this? Also, OP would need to include bucket into their range pack list and a source of water.

I keep a 100% cotton towel in my rifle case for hot barrels.  It keeps the case from melting against the barrel.

These are on sale and relatively cheap. I’ve had good luck with mine.  Have a couple of the transport bags and the hot pad thing.

https://www.mechanix.com/us-en/tactical/