The batteries heat up terribly as well. I am not sure whether the power electronics can dissipate the heat, but they are generally easier to cool than batteries

The batteries heat up terribly as well. I am not sure whether the power electronics can dissipate the heat, but they are generally easier to cool than batteries because the electronics are centralized and smaller. The problem with batteries is that their heating is proportional to the square of their current output, so when you are extracting a lot of energy from them, the batteries get very hot, and there are a lot of them.