Easy fix. Just cut pieces of cardboard the size of the rack and slide it on the underside. So the cardboard would basically be on top of the tub below it. That should help.
Actually... Now that I think about it, I planned on going back and adding panel board to the under-sides of the shelves, so I can do away with the lids. I feel like that in itself will solve this issue and it would sure be a lot easier than ripping off all of the heat tape and adding metal and all of that BS...