As MMario said, I wrap the shawl in a towel to let it absorb some of the moisture. Then I put towels on the guest bed (queen size), then take a couple of large garbage bags (clean and never used, of course!) and cut them open so they will lay flat and put those on top of the towels, then I pin the shawl on top.
So it’s bed, towels, cut up garbage bags, then the shawl. This may not be the best method out there, but it works fine. So far, I haven’t had a problem with the bed getting wet, but I pin the shawl when it is just damp. I don’t own any cool blocking mats, so this will have to do until I can afford something better.