iPhone 4s overheating and suffering from drained battery
I would suggest backing up your phone with iTunes (a whole backup and not only synchronising) and transfer all your purchase. Afterwards, restore the phone with iTunes. 

Test it for a couple days and if the issue is solved, bring back your back up. If the issue reappears, restore it again and re-download your content manually. It might be your user data or settings, or an app making your phone work when it's not supposed to.

If the issue persists even after the clean restore (without bringing back your back up), I suggest to get your device checked at a Genius Bar near you.