Maybe, in my case the phone heats up with any batteries (I've tried 3 different batteries). I think it's a 3G related problem, because with Wifi the phone remains cool and the battery lasts far longer. With no usage, I can do even 3 days, but when I use 3G connection, battery drops very quickly..
Also sometime it drops from 60% to 20% in a few seconds, but maybe that's because the battery is old..
So, the battery is old.