This is crazy but I fixed mine. Here is how it happened
This started several months ago and even fried a battery, I guess from the heat and constant drain.
I have restored from backup, restored by iOS update, even downloaded a iOS from a mirror site.. No change.
Today I downloaded a system status app from the App Store and noticed with everything that was possible to turn off was off, it still had 30-40% CPU usage.
So, I noted all processes that were running then backed the phone up on another computer on iTunes,signed in on my wife's account.Then,although I knew it wouldn't work but I tried to restore it from a saved 6.0 file from my JB days.: note : The phone this was happening to had never been modified in anyway nor any attempts to.
After iTunes extracted the iOS and attempted to verify the restore and which of course failed.i removed phone from charger/sync cable, pulled up the system processes and compared it to the earlier processes and lo and behold.
A process named filecoordination was there when before it was not.The phone had cooled considerably,comparable to my other and the CPU usage has dropped to 4.6-7%. The phone has only dropped 1% in 2 hours.before it would be down to 65-75%.