I tend to use 3mm white opal acrylic. You can create a curve using clamps etc, it depends how 'tight' you want your curve to be. Often the sheet can actually be left flat. As long as the sheet remains evenly illuminated and fills the picture frame it doesn't matter whether it's curved or flat : Obtaining a consistently white background depends on the size and shape of the object you're photographing relative to the size of the acrylic sheet and of course the angle of the camera to the background.
As for the acrylic deforming under the heat of lights, it depends whether you're using hot lights or not. With hot lights, you can use mirrors or reflecting panels both to disperse light evenly across the acrylic sheet and avoid overheating. With studio strobes, simply switch off the modeling lights once you've set up, the flash alone shouldn't generate too much heat.