I'm almost always playing the game (well at least the serious scheduling and strategizing) while charging. However, I do experience my battery getting hot.
I'm assuming the game is constantly in contact with the servers to:
1) send the stuff you're planning to the servers and calculate the impact of your actions to the game
2) receive the stuff other players are doing and calculate what you should be shown / updated about.
I think there are some feature-wise priorities (notification control, being able to put people on a friends list), but this is defenitely where performace could be improved. Speed is fine, stability is fine, just some battery consumption optimisation.