I would not try to do this by hand. I have never tried to shape urethane with heat but I have done other materials. It will be very hard to get this consistent.
At the least, you should make a large clamp. You could use a 2x4 with a notch cut where the end caps on the side skirt are with a bolt to a 2x8 or piece of 1/2 in plywood. I would go further and make a jig using the same idea and adding a second, adjustable clamp. This obviously means you need to take more time. It would make it expensive if you don't have the tools and materials on hand but at least you can get it consistently bent, and replicate the same bend on the other side. By hand, you could could easily have a lumpy mess.
Just a suggestion, it sounds complicated but would be pretty simple to make with basic power tools and would likely yield far better results.