Agreed, what we think is too hot is generally not.
That said, it sounds like you have some potentially glitchy software or user data. the draining is likely from an app not properly hibernating or shutting down. A way to tell is to go under the About screen in the General settings at there's a diags data menu, if you see pages and pages of listings then you've had a crazy amount of crashes and that's generally from bad software.
Be on the look out in that list for any crashes with the word panic. one or two isn't bad but if you have a page or two worth that could be something in the hardware that is bad, including perhaps your battery. sync your sync your data, update your icloud backup etc. (don't forget to verify that your iphotos are imported) , make an appointment or call Apple Care. don't do any kind of restores or data erasing before you go.
otherwise:
I would do a DFU restore because that verifies your firmware is okay. after the sync etc is finished with itunes open, press and hold both the sleep and home buttons until the iPad shuts off and disappears from iTunes. once it does, let go of the sleep button. It will go into what's called 'recovery mode' and have you restore it.
i don't recommend using an itunes backup since they can sometimes grab the bad software and put it back on (if it's coming from user data). either set up as new and just sync stuff or an icloud backup. use it for like 3-4 days. if its still acting up then resync/backup and hit that appointment at the Apple Store. but be sure to wait those few days so there will be diags data for them to see.
