I have heard different things from different people, but here in the South West we do a decent amount of desert hiking.
Protection from bugs is usually little concern because most of the time in the summer day it is too hot for them. So mainly my question is what is cooler to hike in, all else being equal, short sleeves or long sleeves? Any real reason why??
There's a reason desert cultures almost all wear coverings from head to toe.
Three main things to consider:
Despite the convention, "cotton kills," in the desert those same properties (slow drying, water retention) are useful for keeping you cool by slowing down the near instant evaporation in the desert. (See this question for more details.)
To that end: A light colored, loose-fitting, long sleeve cotton shirt will provide the best of all three, with tradeoffs: (more evaporation cooling and sun protection on the arms, but less convection cooling)
However - ultimately sleeve length is personal preference. If you go short (or shirtless ... my favorite (stupidly enough)) be sure to slather on the sunscreen.
Long sleeve, breathable, wicking fabric.
Failing that, long sleeve, ultralight and blousy (loose to allow lots of airflow).
