For anyone new to the thread be sure to go through these steps to address an excessive battery discharge or hea issue. This will clear up any potential corrupt system settings and recalibrate your battery that can cause those kind of issues.
1. Reset all settings (settings app-> general-> reset)
2 a. Go through initial setup steps (lang, wifi, siri, enable location, etc) and choose setup as new phone (don't worry your apps, data, contacts, mail will still be there). Do NOT restore from iCloud or iTunes (It can copy back corrupt settings)
2 b. If you do not get the complete new setup screen with language setup and setup as new phone or restore from iTune/iCloud backup, be sure to go back to #1 and reset all settings again (it should happen the second time)
3. Turn off system location services timezone and iAd (settings -> location services -> system services)
4. Fully discharge battery (until you get the spinning wheel and it shuts off)
5. Fully recharge battery (overnight if possible)
Note, that the battery should run slightly warmer and also take longer to charge than the iPad 2/1. However, it still should not be too hot to comfortably use. If it does not work after a few try's you may have a real battery or hardware issue and should contact Apple. Good Luck!