What size heat tape? We have a large DIY rack made from a plastic shelving unit, and covered the 11"x12" pieces of heat tape with pieces of 12"x12"x.08" acrylic sheet screwed into the rack. Kind of pricey but it worked, and we can easily disassemble and move the rack if needed since the heat tape isn't' actually attached to anything, the acrylic sheet holds it on the shelves.
Tubs are 54 qt under-bed style so they're pretty heavy and the rubbing tub would definitely damage the heat tape if it weren't protected.