If your UTH's are on stats, then you won't have to worry about any damage to the tubs.... immediately. Tubs are cheap though, and they will wear out... I can only speak from my own experience, that I have had 24 15qt Sterilite tubs for a little over a year, and 6 of them get rotated out every week... they're all still fine with heat tape set to 96 degrees 24 hours a day/7 days a week. No warping, no burns, no melting.

The only melting that happens on my tubs is with a soldering iron... ughhh... Still have to burn more holes too...