I'm also experiencing the ipad3 heating issue in the lower-left corner (in portrait with home-button at the bottom).
I have the black 32gb wifi-only, with brightness between 30-50%.. I have charged it once, and while plugged in, installed all my apps, and that was when I first noticed the heat issue. After setup, I left it plugged in to fully charge it. A couple hours later (still plugged in), I turned it on and used the new hi-res Kindle app. After a few minutes I felt the ipad getting warm in the same corner. I figured it was because of charging. So I unplugged it, left it turned off on a table for an hour and let it cool off. Came back and used it to surf google-news (not playing videos or playing media, with Safari the only app running), and after 5 minutes I noticed the warmth again in that lower-left corner. This was never an issue with the ipad1 (never had the ipad2).
Today I ran the following tests:
1 - Unplugged, charge at 98%, brightness at 30%, played youtube video for 10 minutes. The bottom-left corner got mildly warm, barely noticeable (note - it's 68 degrees in the room).
2 - Unplugged, charge at 95%, upped the brightness to 100%, played youtube video for 10 minutes. The bottom-left corner became noticeably warm, maybe 3x warmer than before. The heat is now noticeable on the front glass of the iPad in that bottom-right corner, that's how strong it is. Note - it is nowhere near as hot as the macbooks get running flash or copying large files.
3 - I'm going to deplete the battery to 0%, charge it back up again, and see if that makes a difference (as some have indicated it would). However I doubt this will work, seeing as people claim it is the processor chip, not the battery, that is in that lower-left corner.
I'm surprised that the new ipad 3 has this heating problem. I've been very disappointed at how hot Apple allows their laptops to get (over 200 degrees F!!), while claiming that those are normal operating temperatures. It seems that whoever's running things at apple is completely ignoring the people-factor here. On the one hand, apple touts its philosophy of getting the technological issues out of the way of the users, but then bungles the heat-ratings on their products. Maybe their "human interface guidelines" should assume real people are using these devices and not humanoids with plastic arms and legs.
Unsure right now whether I'll return the ipad 3. I want to know if this is the case with all iPad 3's, or if it's just a few of us experiencing this. I may just get a full-body case for the ipad 3 and be done with it, though sadly this would defeat the purpose of having purchased such a slim device in the first place.