This is a pretty unusual problem, and I've encountered the question in various forums but never the answer. I've had this problem on and off since the Galaxy SII. What happens is I'll take the phone off the charger in the morning, and it will be extremely hot in my pocket all day, then it will die about 10 hours later. This is an intermittent problem. I thought it was loosely associated with the alarm clock, but I got a new phone yesterday because the SIII died a few months ago, and I have not had this phone for more than 24 hours and already it has the same problem.
I haven't installed anything on it, and I've barely used any data. I have a 200 mb plan, so I can't even use data that often. The only other weird thing that's persisted is that the red arrow on the wifi and on mobile data seems to always be lit when I turn on the phone.
Has anyone seen this problem or know how to fix it?