Runs great on my 2012 13" Air, I do fancy graphics and far render distance. I get around 60fps most of the time but it can drop lower, never to unplayable framerates though. I haven't ever experienced my computer getting overly hot because of playing the game, but it does warm up and the fans do crank up pretty loud if you try to run it on the higher graphics settings. There are probably better computers to play Minecraft on, but the 2012 Air can certainly do the job.
(As an aside, I really don't recommend playing with the trackpad as your pointing device. I hope you're using an external mouse.)