The desert has seasons like every other biome (having lived and worked in various deserts - outside LA, AZ, NM, far west TX, and Kuwait/Iraq). One constant, I usually go with long pants after much experience with Thorns. Unless it is summer, I usually pack my mostly Patagonia layering system just due to wickiness , though I do have a snag-resistant zip T from MH if thorns are expected. Otherwise, in summer any old poly-cotton will do though i keep a synthetic shirt packed in case of rain. All in light colors. The high deserts (Chihuahuan/Great Basin) can be different (colder/dryer)than the low deserts (Sonoran/Californian), so I would ask you provide more geographic specificity. Summer is a rainy season so that needs to be accounted for though the Sonoran has more rain. Similarly there were even massive puddles sticking around a Bedouin tent in Kuwait( next to the Persian Gulf), so there may be a need for rain gear depending. Even in the US, check the weather. Deserts can get cold at night so don't forget insulation and checking the weather (when I returned to the US, I ran into snow from the outskirts of Los Angeles all the way to my base in El Paso. 1 month later, El Paso was colder than Green Bay.)
Add: maybe TMI but the desert is not always hot and dry.