I've been reading and watching this issue progress and have started to see some trends. It appears to be left from some corrupt settings from a previous version of iOS and also a recalibration of the battery. Couple this with a post from another user (davidch), here is what is largely considered a solution to the issue...
1. Reset all user data (settings app-> general-> reset)
2. Go through initial setup steps and choose setup as new phone. Do NOT restore from an old backup at this stage, it may write back your corrupt settings.
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). This may take some time.
5. Fully recharge battery overnight.
Please give this a go before you take the iPad back. If it resolves the issue then it certainly points to the software running processor controls for the iPad 2 which has different needs to the new iPad or indeed a battery recycle issue.
Feed back your experience below on this post and let's see if we can get the feedback to apple so they can coordinate an iOS update if needed.
Don't forget you also need to recycle the battery.
I do agree however that it gets quite warm if the brightness is full on with auto switched off, playing 3D games. Mine got hotter so I turned the brightness half way and then it was warm but ok. To me that is just a function of the extra power tho