I believe the problem is related to cellular data and possibly LTE speck ally.
I was just put of the country and therefore had my cellular data off and only used wifi. My battery lasted FOREVER and my phone never got hot.
Or, maybe it's related to a signal reconnect concept - if the phone has a weak signal to its wifi or wireless network the. I think there is a bug in the software where it spends all of its resources trying to reconnect.
I remember this happening to me once with my iPhone 4 while on a plane. I forgot to put my phone in airplanes mode and when I landed and took my phone out of my pocket the phone was REALLY hot And the battery was dead.
Hopefully Apple will have a software fix, but in the meantime if you are on wifi try disabling your cellular data and see if the phone runs better.