I made mine with 3/8 inch plywood - wasn't thinking about the warp factor, more the lift factor. But I also built a frame on the bottom of it to keep it in place on the ironing board (you can see pictures on my blog - linked below). I put down a wool blanket and then the silver cloth. I've thrown a piece of muslin over it that can be easily washed as I've been using lots of starch.
Alternately, you could use a layer of warm & natural batting covered with Duck Cloth (as was recommended to me by Harriet Hargrave)
Cheers, K