Well, we all know that the battery is far larger than the orignal iPad or iPad 2 due to the amount of juice that it takes to light up that pretty new display and run that new quad-core GPU. A lithium-polymer battery is used in the new iPad just as it is in every other moble device, and if you understand how these batteries work, then it would make perfect sense as to why the new iPad runs warmer, or hot depending on your interpritation or sensitivity.
Batteries use electrolytes that require "exercising" to get the most longivity, both day to day and for the life of the battery. Heat is created during the process of excersing the battery, or while you use or charge the device. The left side of the iPad is where the logic board is located, and the exact spot where it gets hottest is more than likely where the battery connects to the board, which could be considered the "gateway" of where all of the battery's energy is flowing to, which would explain why that spot gets hottest, sort of like how your catalytic converter on your car gets blazingly hot because that's where all of the exaust from the engine is first constricted or bottled-necked.
Naturally, the faster the battery drains, the faster it gets warm/ hot, much like friction. So if you're playing a 3D action game for hours on end, then you can expect the processor to be under more duress as well as the electrolytes to be exercised that much quicker, which in turns depletes the battery that much quicker and causes a much hotter battery than you would find breifly checking emails or lightly surfing the web. Think of it like trying to start a fire the old school way with a stick running back and forth against another flat piece of wood - if your surfing the web for a few minutes or checking emails then it's the same as lightly to moderately running the stick back and forth, but if you're playing a 3D game then you're vigorously running the stick back and forth and you'll probably get that fire that you were hoping for.
I know that this isn't a super scientific answer, but it is common sense: The battery is bigger, which means that there is a lot more electrolytes that create heat when used or recharged, and if there are more electrolytes then it can only get hotter under more duress.
I obviously have no idea if this is a firmware issue that can be corrected by an update (much like the 4S battery issues), but since the iPad is using the same OS as every other Apple mobile device that is capable of running iOS 5 and we're not seeing a flood of new heat issues for iPhones or iPods with the latest 5.1 update, I'm guessing that it's due to the larger battery and the amount of power required to light up the highest resolution display currently available on the market across all devices (less the rare 4000k display) as well as the software that the ipad is capable of running, such as the Infinity Blade series. Side note: For those of you that don't know, firmware is the software that runs the hardware, in the simplest definition. If there is a bug in the firmware, one of the many affects that you would see is a hot battery or poor battery life.