My battery does not stand long (one day max), but I don't know if the battery is new (the phone is "refurbished") and I frequently use Quasseldroid, Xabber that try to stay "connected" all the time, and the 3G network (sometimes I switch to "2G only" to save battery, but other times I switch back to 3G and stay there).
In any case, note that I installed the nonfree firmware and that could make a difference too.
I didn't realise about overheating, I guess I don't experience it.