Desert Wind I can think of three alternatives.
Cold damage because while deserts are climatically the hottest places on earth...they are only so during the day. At night, deserts can become almost inhospitably cold. Especially when the wind blows across them at night.
Electricity damage - the idea of the school is to focus on speed and mobility. Now, sure, fire can spread pretty quickly...but is fire faster than lightning? If you had to pick the five standard elements of D&D (Acid, Cold, Electricity, Fire, Sound), Electricity is probably the fastest out of all of them.
Sonic: probably the weakest of my arguments here, but the name of the school is Desert Wind. And you can't see the wind, but boy you can hear it - invisible, but perceptible. Doesn't that seem like sound? In addition (I admit, I write this in less than ideal frame of mind), the wind picks up little pieces of sand out in the desert, which is why all those desert nomads have to wear the full-body clothing: so they're not cut to pieces by flying grains of sand. With the exception of a pure force effect, the thing that would come closest to simulating that would be sound energy. Especially since we now that sound is just a vibration, energy moving through the air.