The "Mongolian" tent is called a yurt. And the Mongolian steppe's isn't even close to the same climate as Iraq. Might be a match for northern Afghanistan.
The Gobi is ridiculously varied (as is Mongolian really, it was wrong of me to generalize that much). That said, the Gobi is a relatively cold desert. High elevation plus relatively high latitude. My geography is kinda sketchy, so a quick google tells me that while the hottest part of the year can reach +30C (I guess approaching Iraq levels), temperatures in the north (the Mongolian part) are generally lower, and infact, you would probably be far more worried about how cold it gets than how hot (the famous Mongolian winters???).
Unfortunately, I can't really answer for the Bedouin.
hm I just looked at the wikipedia page quoting extreme temperatures up to 50°C but the challenge in the desert definitely is the huge fluctuation - considering it can go down as far as −40°C for Gobi.
Overall, this sounds like another point for thick, heavy tents (or in terms of the urban jungle: thick brick walls here in Europe keep wonderfully cool in summer and warm in winter.)
But I can also see how the a/c is probably one thing they do for keeping morale up... so this might not only be a thermic/physical problem.
