You can download a free XDA version of BBS (BetterBatteryStats) - [APP] [04 Aug - V18.104.22.168] BetterBatteryStats adds battery history back to Android - xda-developers
- in the second post; must be registered. Get the first one, not the others - they are beta I believe, and they crash on my S3 when installed.
Check to see if you have a process called Factory Test, or Factory Mode. When BBS is installed, check to see what percentage it is showing.
I downloaded WatchDog Lite app to check what was going on, and it alerted me that Factory Test was using over 45% CPU constantly overnight. My S3 went from 100% to about 66% overnight without ever touching it.