If you're sure it's plastic, be careful with the heat. Depending on the age, may be celluloid, which I believe is a product made from plant matter. Might try Googling an appropriate subject matter. Some on this forum have had success bleaching what seems to be celluloid, but flattenning, I don't recall. I would think a very hot water bath, and then clamping between 2 pieces of glass surfaces might help. Even low temp in an oven would heat the whole piece, and avoid warping from the application of uneven heat from a heat gun or similar device. Might even apply the clamping with glass before heating in an oven.
:I have a nice old Cromwell radio that has a wood case and a plastic front. The plastic is not broken, but it is pretty warped. Is there any way to straighten it out? I thought of heating it VERY gently and clamping it, but I'm not sure.