This is how power line deicing works on systems overseas. You need two legs to the circuit, so it would involve either isolating lines from each other on double track, or earthing out the end of the lines, and using the tracks as a return path.
The option I was actually thinking about was having a heated pantograph of some type.
If she refuses to resign, it will be interesting to see if greens use the "waka jumping" rules against her.
They were against them at the time, as they felt they could be used to silence dissent in the party ranks, so to use them would be an embarassing change of direction for them.