My phone get hot easily too..
So far after 2 days of usage I can say that the battery life is quite good
I think its the phone that heats up, not the battery. When installing apps and such, it tends to heat up, especially the camera and the screen. Fortunately because of the leather back, it feels fine in the hand.
Anyway, gotta say I am impress with the battery for now. Overnight, I stopped charging around 10 pm, and I had to restart my phone a couple of times after that due to encryption. This morning when I got up to check, its still a healthy 97%. My Z3 Compact would have lost at least 9% battery overnight. But it remains to be seen, how well will the battery last over time, andas we install more applications. I feel that one of the problem for Android vs iOS is the background app sapping the battery faster. So the more apps you have, and depending on what kindda apps, the faster the drop. Not sure if anyone have the same kind of experience.