I have all my larger mats stored on their sides next to the refrigerator. A nice little spot there and out of the way. No problems there. But once I put a hot coffee cup on a 24 inch mat. Big warped corner :-(
Then I read about how to fix it. Put it on a piece of plywood and put a heavy piece of glass over it. Lay it in the hot sun all day. (We had a lot of that last summer.) Carefully bring it inside and let it cool off naturally. That took care of my warp. You can still see where it was because it had been there for years, and the color changed where it was higher, but it is now usable.
Now, don't you all have a piece of heavy glass just lying around somewhere? ? ? We used to have Clear View windows in our house. They used pieces of plate glass that slid open. So I have a few of those that aren't broken.
I would think an ordinary piece of glass would work, too. It's the heat you want.