Wow. Nobody wants to touch this one. I'll give it a stab there.
Touchy subject, literally.
Personally, I would not. The ID liner is EXTREMELY heat sensitive and simply warming them may be enough to loose the mold, not to mention IF the bag was put on hot, and kept there for a while. you'd be looking at a new set of liners. The EVA foam is thermally- active at 100 degrees Farenheit. I don't care that the manufacturer says that it molds at 212 degrees.
Keep them at room temp or under your car heater in front seat and you will never have any worries.