There are myriads of Android power saving tips out there. Same symptoms, my battery was draining very quickly and I made several complaints to Google. It was also getting hot very quickly -- too hot for comfort.
This one is specifically for an issue I had on Samsung Galaxy SIII. The battery drains rather quickly and going to the battery view, I found that Google+ was draining a huge portion of my battery. If you don't usually use your GPS, read on.
I was not using google+ but it seems that I can solve this by following the below steps.
As you can see, after turning it off, for the rest of the day, the Google+ app takes less of the battery. It is still eating my battery although I don't use the app. Do tell if you know how to uninstall it as it seems to be a core app that cannot be uninstalled.