Today, 03/20/2012 I went to the Apple Store and conducted my own iPad3 heat investigation. The iPad3 table had about a dozen tablets which were running at maximum brightness.
The back of the unit in portrait position was slightly warm in the lower left quadrant as discussed on numerous websites. The heat was NOT excessive or uncomfortable in my opinion. Remember these machines run all day long with no screen saver engaged. I also spoke with some informed persons in the store who stated that there were no overly concerned customers running back to return their iPad3 purchases.
Causes of heat- faster processors, larger battery and related charging circuts,cellular circuts and much brighter screen capabilities. Speed and light generate heat. Firmware/software upgrades will be released at some point to streamline the assorted processes in the tablet.
Heat reduction methods-
1.Go into your iPad3 "Brightness and Wallpaper" settings; lower your brightness a little bit.
This will make the screen last longer and save battery life.
2.Go into the iPad3 "General" settings for "Auto-lock" and make sure it will engage after 15 minutes of activity. This will dial down processor requirements as this screen saver setting kicks in during inactive periods.
3. If you get a chance go check out the iPad3 issue at the store display nearest you. I think you will find this issue to be a "non-event" dispite media attempts to generate "Apple iPad3 panic" in the consumer market.
Disclosure: I am long AAPL.