I would suggest using melamine or PVC for the rack. Alternatively if you are willing to use a lid-on-tub design you can just get a regular plastic shelving unit and cut the legs down to the point where the bins can just fit between the shelves; I did this for a 54-qt five-level rack as it ended up half the price of even melamine and it comes apart easily if I need to move or store it.
Heat tape goes on the shelf of the rack under the bin.
Only one thermostat needed since each piece of tape should be the same size, or the tape is threaded along the shelves.