I would wire it separate. you also want to protect the heat tape (flexwatt) from your tub sliding across it. the plastic is very thin and can be damage quickly. I was thinking one time of making racks with belly heat. I was thinking of using roof flashing over the heat tape to protect it from the sliding tub. its thin will transfer heat and you can buy it in a few different sizes at lowes or home depot. just something for you to think about.