UTH use radiant heat. Plastic is an insulator, not a good conductor. So I'd imagine using UTH with a plastic tub is a very inefficient way to heat. UTH work with glass because glass will transfer more heat. There's no way you're going to get heat anywhere but directly over the UTH, and you're going to waste a lot of electricity for that heat.
I'd recommend using some kind of heat lamp if you're going to use a plastic tub.
Besides that there's the fact that many plastics release carcinogens when they're heated. I'd do some research and find out which plastics are safe, if it were me.