If you tell the hotel that you have a restricted medical diet then you might be surprised at how willing the hotel is to allow you to put food in their refrigerator. It also wouldn't surprise me if the hotel actually does have a set of microwaves and min-fridges that they just don't admit to having unless you push a little bit. Call the hotel and if the first person whom you speak to isn't willing to help then ask for a manager.
Worse case scenario is you ship a cooler to yourself and fill it up with ice from the ice machine. Microwaves are cheap these days.
By the way, the "find me gluten free" app is very helpful for finding places that sell gluten free products and or have gluten free menus. You can see a web based version of the app if you google "find me gluten free".