Not quite as obvious but very effective solution: Iron (the kind you use for ironing shirts).
Seriously, it works. Drain it of all water and start it on a medium setting (around 150F). Then work up towards linen.
But unfortunately the plastics you would be using such a technique for are not terribly strong (acrylic specifically). If you want to thermoform a contoured shape that's durable you will probably want to go with slightly thicker ABS plastic. Then add a window made out of really thin polycarbonate
Let me know if you have any plastic-related questions. I've written a few introductory guides to plastics machining.
http://nerfhaven.com/forums/index.php?showtopic=8007