Since no work is being done directly by the heating coil (it is not moving anything against a force), there does not appear to be any other form of potential energy in the problem except for that provided by the voltage. When this potential energy from the voltage gradient is lost as the electrons move through the resistor, it must form the only other kind of mechanical energy there is -- kinetic energy. In other words, the loss of potential energy must make something move. The only availble things are the molecules in the heating coil. In this case, the current passing through makes them vibrate.