When these 2 are connected and the MBP's lid is closed, does the MBP drive both displays at same time, or, is the internal display Off?

I'm concerned about the MBP generating more heat, when the lid is closed, than is good for such extended manner of use.

I do that all the time with a 23" LCD display and my early 2011 MBP. The laptop's display is indeed off and the menubar, windows, and such are exclusively on the monitor when the lid is closed. I had the same setup with my older 2008 MBP and used it that way every day, all day.

Apple provides directions to do so, and the newer displays even have a laptop magnetic power connector, so it is fully supported and safe use.

That all said, I would not use the MBP as a table and pile papers or anything on it, nor would I block the vents. As long as it has space all around it for air to pull heat off the metal, you will be just fine.

Thanks for the confirmation.