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.

iOS 16 finally brings haptic keyboard feedback to your iPhone
Wish you could have feedback while typing on your iPhone without bothering others around you? The new haptic keyboard feedback setting in iOS 16 is the answer.

Apple's HomePod could get an iPhone feature you use every day
Those hoping for a revival of the OG HomePod could be in for a treat if recent reports of a return are any indication. A new report now claims that the updated HomePod will not only be more like the original smart speaker than the smaller HomePod mini, but also suggests a big iPhone feature is being added.

Five more M2-powered Macs are in the works, says well-connected journo
Apple already has two M2-powered machines but it's still working on getting a further five into the market, according to a new report.

Take an Apple Watch charger on the road with you
Looking for an Apple Watch charger to take with you while you’re out and about? Check out these portable chargers!