There's a reason desert cultures almost all wear coverings from head to toe.
Three main things to consider:
- Protection from the sun's harmful rays.
- Air flow for convection cooling
- Moisture retention (you heard that right) for evaporative cooling.
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.