Sorry upand, not sure you understand my intent or the process involved, heating a stone and directly applying it to polypro is about the worst possible thing you could do, even worse than the hot air gun I was using.
I successfully annealed the box in my home oven. I preheated the oven to 170 to avoid setting the cardboard on fire from direct IR from the primary heating coil (the cardboard will be clear later). The PDF file I linked recommend you gently increase the temperature and use fan forced air but I had no problem with passive convection. Once it was preheated I put a couple sheets of cardboard in to avoid direct IR exposure to the plastic box and placed the box on top of the cardboard on the center rack. After an hour the temp was only 180 (as read by an IR non contact thermometer) so I set the oven set point up to 180. The peak temperature measured was about 190 degrees. I let it sit at the 180 oven set point (which resulted in the 190 temperature reading from my IR gun) for about 30 minutes and then shut the oven off, about two hours later it was down to near 110 degrees so I popped it out and set it aside.
The side only had the slightest hint of a wave left to it when I took it out, and after it open air cooled it was straight as an arrow, I can't even tell which drawer it was anymore.
Please note, I'm not entirely sure this process will work with crosslinked polypro but most consumer devices don't use crosslinked polypro.