Ignore the users saying the new MBA can't play games. It can play current games very well and you'll probably be covered for the next couple of years of game releases.
I didn't buy my Air for only games, but personally I do play a fair bit of Diablo 3 and Starcraft 2 and its wonderful. The users stating that the Air is worthless for games are probably graphics whores that need the game to run on EXTREME settings or else they might as well just kill themselves than play on anything below that. Medium to High and even low for future games are perfect for me. I am just happy to be able to play.
Does the Air get warm? Yes, nothing you can't touch though, it is by far the coolest running laptop I've owned, even when playing SC2 on high settings.