Would it be possible to use heat to get it to float, instead of helium? Heat it up with electricity.

Sure, that would be possible. The generators themselves will produce a fair amount of heat. It’s also going to have a fair amount of passive lift, as it’s essentially a kite. So simply being able to maintain a rigid shape and airfoil will do a lot to produce the desired lift.

I have to wonder though, how much the power transmission lines weigh, that seems like a serious limiting factor on maximum attainable altitude.

The transmission line question is interesting though, there’s a complex optimization calculation there. Traditionally with wind, larger turbines are more efficient. As you increase the turbine blade size, the area that the blades cover (and thus power generation potential) increases more than the mass of the blades do. So the result is (generally speaking) a larger wind turbine is more efficient than a smaller one. But now factor in the transmission line… The larger the turbine the more power it generates AND the thicker (and heavier) the transmission line has to be for its entire length. To complicate things more, higher altitudes mean stronger and more reliable wind. So now how do you optimize for turbine size/cable gauge, and cable length/altitude?

It seems tricky, but like perhaps there’s just a right answer, an optimal size.