Still an interesting hypothetical question though. Maybe you could achieve the same effect more easily with mirrors.
if you actually want to prevent light from becoming thermal energy on earth it'd be far easier to build a dyson swarm to obstruct the sun.
A mirror would also be much more effective if part of some ring like structure orbiting the earth, as most of the energy would never enter encounter earth's atmosphere in the first place.
> exporting that heat into the rest of earth (where it is used and expelled as heat)
Once you release the stored energy it's a different story.
You could even achieve a similar effect with today's tech by running solar-powered heat pumps that pump the heat into deep bore holes or old oil wells.
But that air conditioning the desert is a particularly great idea, but compared to better ideas like putting translucent reflective foil into orbit it had the charm that it has local effects you can achieve without international cooperation or incident