Thank you all for your comments. I knew I would get some good advice from Gransnet! The video was very helpful, NotSpaghetti, I'm going to give that a go, maybe using a damp pressing cloth to add some moisture as well as steam from the iron.
I do think the quality of these mats varies enormously. I had another older mat that never warped even when left in a sunny spot but its self-healing properties were not so good so it had a few deep cuts/chips that I had to avoid when using it. It's now under the bed as I'm keeping it "just in case" 