Taking aside you certainly can do radiative cooling in desert at night just fine - you have air, which even if hot to desert standards during the day is still by magnitudes more effective for cooling via direct heat transfer than radiating heat away in vacuum.

I did realize geothermal would be the way to do it in the desert; the ground is still typically cooler than the heat computers give off.

It's still problematic that most deserts dont haveaccess to groundwater, so bootstraping and maintenance are an issue.

You can try to put the heat underground. Maybe there is an aquifer you can use. Or maybe your desert is close to the coast!

Still easier than radiating it into space.