Oh man, that's so unusual. The most common things to try are checking your settings such as making sure the screen brightness isn't all the way up, as well as turning Bluetooth, and Wi-F off if you aren't using them. You would also want to uninstall any unneeded 3rd party apps like battery manager applications. If the phone has a removable battery, you could try testing another one to see if a replacement does the trick.
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