Here's something else odd: Mine has been in the dock since I opened the box. It's charging and restoring my previous iPad's backup, so gigs and gigs of stuff is being installed.
It was warm on the bottom left. Not hot, as I said, but warm enough that I noticed and was surprised.
Now, it's definitely cooler (still installing that backup - almost done), but it's warmer on the bottom-right side.
Again, it's not hot. It's not even laptop computer warm - just warmer than I was used to with my previous iPad 2, which I sold 2 weeks ago, so I can't compare.
This makes me suspect it's the battery...? Supposedly, the battery is something like 70% more powerful than the previous iPad 2's battery (but performance is supposedly the same due to things like the retina display consuming more power).