According to the Fiskar site they recommend placing cookie sheets in the freezer and then laying the mat on a flat surface, cover with the frozen cookie sheets and place a heavy object on top of that. Leave it until the cookie sheets reach room temperature. They advise not to use heat as it will make it worse.
I have a warped cutting mat at my other home and I am going to try the cookie sheet method when I get there. I took good care of that mat and have no idea of why it warped but I have tried keeping it weighted on a flat surface when I'm not using it and it will look like it flatted it out until I start to use it and the warp is back.
I'm anxious to know if anyone has used the frozen cookie sheet method and if it worked.
Great idea Jan for the carry case/design board.