My original prototypes had 3 layers of fabric (lining, Insul, and outer fabric) when on a winter backpacking trip a light bulb clicked on, and I realized I didn't need the lining.
It has worked just fine, lining touching the heat. Insul is designed to take heat to a point (it is used without a lining to be tea cozies for instance). Insul breathes as well, and it works well being near the heat so it can shed condensation. I have test washed cozies in the washer and dryer as well numerous times, and the Insul holds up well to the blasting heat (though it dries so fast that I just machine wash and air dry my own cozies).
My personal cozy I use on trips sees use about 2-3 times a week, and has been machine washed about 10 times so far. It is still looking pretty good (especially since I have dumped food on it a number of times!)