My original iPad and iPad 2 have always been remarkably cool, even when playing graphically intensive games or high definition video, but my new iPad is getting a little warm to the touch. It's by no means as hot as my iPhone 4s gets, which can be really hot if there's bad reception or I'm tethering. It's also nothing like how hot a MacBook gets when playing Adobe Flash. But hotter than my old iPads which were absolutely cool all the time. Since other devices routinely get warm or hot without issue, it doesn't seem to be anything to worry about -- if anything it might just be a sign we're finally pushing iPads as hard as we've been pushing our other gear for years.
The heat seems to be along the left hand side (if you're holding it in portrait mode with the home button at the bottom. I don't think it's the LTE radio because it feels the same on Wi-Fi. According to the pictures iFixit posted during their teardown, the iPad's board, including its A5X system-on-a-chip appear to be along the left hand side. (The gigantic battery is on the right.) The A5X includes a quad-core GPU, but I'm not doing anything particularly intense when the iPad is warm (just downloading apps right now).
We're talking about this now in our [iPad 3 forums] and have a couple of great threads going:
If you haven't already, jump in there and let us know your experience with heat on your new iPad.