Frankly the MBA is a poor platform for gaming. The only time I have had a core shutdown was this past weekend when I tried running the demo of 'Build-a-lot' for about 45 minutes and the entire system went to sleep when the cpu hit 95 degrees. Horde of Orcs really runs the temp way up as well.
I have been playing battle for Wesnoth a bit (someone else pointed it out) and that game has me hooked, and runs just fine.
The conclusion I have reached is anything with graphics that involve constant motion really seems to pop the CPU and thus heat the system up an inordinate amount. Turn based stuff seems to be fine for the most part. As most games require constant motion this is certainly impactful on the effectiveness of the MBA as a gaming machine.
I can't imagine trying to fire up WoW for any period of time. I'm sure it would run, but I trust the system could only handle it for an hour at the most before overheating.
Something is definitely wrong with your MBA because no Mac can overheat just from running something intensive.