You can of course choose to just assume things and be happy with the decisions you make based on your assumptions or you can actually look into the issue a bit and perhaps discover that it might not have anything to do with the Air itself:
https://us.battle.net/forums/en/hearthstone/topic/20755765770 and
https://www.reddit.com/r/macgaming/comments/4o2q6w/hearthstone_macbook_pro_hot/ and and and...
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In theory, the processor could be just fine without the fan altogether. Why did they add it? Because in the situation when one would push the system for a longer timespan, then the fan can actually help keep temperatures more stable, which also means more stable performance (you don't get throttling so fast, or maybe at all). Why is this important? Because it clearly places the Air between the Macbook and Macbook Pro.
I have to agree with @
darkmatter343's comment, meaning that if you're really pushing the machine so often to its limits that temperature is really a constant issue, then either the apps you are using are not well optimised for Mac or they are indeed that demanding in which case, you might have gotten the wrong notebook for the job. It happens...
I develop enterprise level software for a living and do all kind of other projects on the side (web, desktop, mobile dev... you name it) that also include light to medium graphic design and video editing and the new Air is more than capable of handling the stuff I throw at it (+ even some light gaming, but I do have a desktop PC for that). Would a Pro handle things better, would it be perhaps significantly faster in certain situations? Definitely... is one mandatory for my job / needs? Clearly not... so if you're not happy with it, then just get something else. Thankfully, Apple isn't the only brand on the market and nor is it the cheapest or even the one with the most performant devices...
There's no point in dramatizing the situation, no single device will ever fit all needs.