Unfortunately, its normal for iPad 3. Normal does not mean its good though. My iPad 2 runs completely cool at full brightness. This is one of the things that is a step backwards with the new iPad IMO.
Well that was stupid of me. I just voted no, as in "Do I have a defective iPad—No." but just realised that your question there was "Is it normal for the iPad 3 to get warm on maximum brightness?" to which the answer is yes.
In future, it might be best to keep the same question on the poll as the topic title, or at least keep the same intent rather than flipping it around.
But back to the question at hand, this is completely normal, especially if you're doing more complex tasks like playing games. The Pinball Arcade at max brightness will warm up my iPad in no time for example. (but I would never describe it as hot—cooler than any notebook I've ever used—especially if they're running games)
You've never tried to use it during the day or near a window? I definitely need to turn the brightness up full sometimes, and this is in Northern Europe, which isn't exactly known for its sunshine.
I have one of those remote laser infrared thermometers. My iPad 3 typically gets to around 83 degrees F. It doesn't seem to change based on screen brightness though.
Still cooler than the VoIP phone I got at work. Just sitting idle, it registers a balmy 91.5 degrees. 🙂