If they're modeled after the real Middle East ... well, that could be anything.
Nubian and other African spearmen were normally light or no armor, usually just spear and shield. Egypt tried a little harder to armor their troops, but for most of their history, the infantry was mostly light.
While the Mamluk (Saracen, and later several Dynasties in Egypt) were primarily medium horse archers, it would certainly be inaccurate to call their armor light. They were hit-and-run horse archers, true, but not light. Same with the Ghulam (warrior-slaves of the Islamic caliphates) - they tended toward heavy lamellar armors and battle axes. (Many who read about the Crusades period fail to realize that the elite of the Saracens were actually more heavily equipped than their European counterparts.)
On the far extreme were the Persian and Armenian "cataphract" horse. They were extremely heavily armored, both man and horse ... and while they fell out of use about the time of the Crusades (for unknown reasons, probably economic), they ate alive just about every army they encountered before that, even giving the Legions of Rome the fight of their lives. However, they were not the backbone of the Persian army - the bulk of the Persians were based around lighter horse archers and light spearmen. But they weren't something you really needed a whole lot of ... like war elephants, just a few would get just about any enemy commander's undivided attention.
So while the pattern of the Middle East was Asiatic, in the sense of encouraging mobility over durability, it was not a fixed rule nor was the concept uniformly applied. The idea that all Arab fighters went out there in silk shirts is a myth... many were wearing 60 pounds of very sturdy lamellar armor.
The myth probably got started by observing seagoing pirates. North Africa has been producing pirates forever, and obviously many sailors tend to be nervous about wearing armor, as it gets real hard to swim if you fall in the ocean. How the idea of Barbary Coast pirates got expanded to include stories about land-based armies is a mystery. (Oddly enough, the Japanese navy of this time refused to give up their armor, and just tied themselves to the boat with safety lines.... but that was not so popular in Europe/Africa either.)
However, it is a myth that many fiction writers continue to play upon (because people expect it, and it seems to make sense) ... so just because history won't back that up, don't assume that applies to the novels in question.
But as for temperature control, any armor (leather, steel, or whatever) and probably even unarmored people are going to need a light-colored tabbard or heavy robe of an insulative material (wool is good) to keep the sun off. The desert sun will cook you, I promise. (I'm sitting in Xi'an, half way between the Gobi and the Takla Makan - and I don't go out in the summer without a hat.) But it will cook you no matter what armor you do or do not wear.
