Just to make sure you have the best advice, talk to the Ultraheat people. They are helpful and it only costs a little of your time. They have lots more experience than those of us on this forum, even those who have Ultraheat pads.
I have the dual voltage pads on my tanks and have never had any problems. My understanding is that they should not get HOT and if you have something in your tank, it should never damage the tank. The pads are supposed to be thermostatically controlled, on at 44* off at 64*. Red and white wires are the 12V wires; a black electrical cord with a male plug for a receptacle would be for the 120V circuit, at least that's the way mine came from Ultraheat.
It's pretty clear that you have a wiring problem, but exactly what it is isn't clear, at least to me. My GUESS would be that it's in the 12V circuit, like maybe wired directly to the battery, but not having seen it, my opinion isn't worth much in this case.