Don't recommend the sand, or you'll end up with scratches. The glass beads they use for bending plastic eyeglass frames is a possible candidate, but don't where you'd find it. If it is truly flat, gentle heating while clamped between 2 glass panels should help. You could try 2 cycles by gently clamping and heating in an oven (150-200 degrees), then cool while clamped. Then apply stronger clamping the second time. If its polystyrene, might Google it to find best melting/working temps.
:::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.
:Try this again. with feeling.
:The radio appears to be from the 50's so I don't think it is celluloid. It is most likely styrene. The real problem is it is louvered in the front so there is no real flat spot to clamp it. I'll see if I can come up with a jig of some sort. I may warm it in an oven, or I could rig up a sand bath. I have tried water on some other plastics and had back luck because the water softened the plastic too much.