UTH's don't get anywhere near enough to melt plastic - at least they shouldn't, and once you get it on a thermostat you're safe in that regard. I also think most tubs have short little feet that prevent them being smacked down flat against the shelf below it, but I'm not 100% sure on that one.

Either way, they're warm but they're not hot enough when used safely (with a thermostat set appropriately) to start a fire or melt plastic.