Like it was mentioned before, make sure you have something to regulate your heat pad. At the very least a dimmer is needed, but you need to be really responsible to use that. If your house fluctuates in temp the dimmer will not adjust for that, so you may have to adjust the dimmer twice a day. A thermostat would be easier because it will adjust for temp changes in your house, but if you are going to spend less than $60 on one, you might as well get a lamp dimmer. Cheap thermostats are a waist of money. I suggest not buying anything cheaper than a Ranco or Johnson (thermostats).
And no you don't need anything between the tub and the heat pad. The heat pad will not get hot enough to melt the tub, plastic melts at 400+ degrees.