The UTH won't melt the plastic because you'll have a t-stat hooked up to it to keep it from getting too hot. If it's safe for your snake, it's safe for the plastic!![]()
The thermometer unit should be sitting directly on the floor of the tub, so that gives you a pretty good idea what your cool side temps are. The accurate belly temps are most important on the warm side. Once you get your basic temperature gradient dialed in and consistent, you can move the little probe on the end of the wire around sometimes to spot check temps in other parts of the enclosure if you want.
I would highly recommend a Johnson t-stat that's already wired for you to plug in. That should run you about $70 and will by far be the most expensive piece of the puzzle. You should easily be able to put together a very nice tub for less than $200.