What heat resistant plastic should I use for a lightbox?
I'm not sure if you are still looking for strips but using these may help you with the heat problem. 

 

They are slim, 7/8" by 1-5/8", not overly expensive and have a lens over them. They can even be mounted on their sides.  These would be cooler to run.  On the plastic, I'm not sure if just want to color the light or turn it into a part of the art piece, like lighting the ends for effects like that. 

The nice thing is that there are similar brands so you can get something similar in you area.  Another type of lighting you can use is LED, but it would be 3 or 4 times the price of these.

On the plastic you can always use a piece of opaque white lens from recessed lighting.  You should be able to get them at a lighting store or at a DIY box store, or even an arts and crafts store.