An UTH does not generally have the heat to melt a sterilite tub. Certainly not at 92 degrees. Even an unregulated (plugged directly into the wall) UTH shouldn't melt the tub barring some kind of malfunction (though it would obviously burn the snake).
Definitely wont melt the tub. Before I got my rack put together I had UTHs on all my tubs with no problems, and I still do when I quarantine snakes. They are controlled by a thermostat.