I had to flatten all my plastics of my pinball only a few months ago which were very warped.
I bought a heatgun from Bunnings which was probably less then $20. Used the low settings and started well away from the plastic. I was suprised how little heat it needed to bend and I was careful not to overheat as I did not want to do any damage to the artwork (which was on the bottom).
Once it was starting to bent I clamped it in to position. And let it stand for say 30 mins. Some of the badly warped pieces I had to repeat this process a couple of times. Each time it got better and better.
Anyway, no damage was made to any of the plastics and they looked 100x better.
Thanks Mark