Desertification is a measure of rainfall, not of temperature. And it is a local measure, not a global one.
A change in the global average temperature has a lot of different immediate effects, and those effects also have effects. Rainfall changes are a good example. Where it is already dry, a temperature increase causes less precipitation. Where it is already wet (such as oceans[citation needed]), a temperature increase also increases evaporation, which in turn can cause more rainfall downwind.
I said deserts expanding, and temperature is also a local measure, global average temperature has no more effect on anything than global average density or global average specific heat. "I can swim because my density is lower than the global average density" is nonsense. "It's raining more because the global average average kinetic energy distribution went up" is also nonsense. There is no sense in claiming there is any sort of dynamic effect at location b (which remains at 289 K for this explanation) because the temperature at location a went from 291 to 292 K and the temperature at location c went from 273 K to 275 K. Can you do math on the temperature of a bucket of ice cubes and a kettle of boiling water and declare the average to be ~323 K? Sure, would that be a nice warm bath? Indeed. Would you enjoy hopping into a tub of water that had just been filled halfway with ice cubes and halfway with boiling water? Probably not, intensive properties don't work that way.
If deserts are expanding then the planet is getting cooler.
If deserts are shrinking then the planet is getting warmer.
Not sure if you're confused on what a desert is, confused on what the climate is, or are thinking of some obscure atmospheric thing that is probably being overapplied here but definitely needs more thorough justification and explanation.
A desert is a region with precipitation below a certain level, less than 25 cm a year as I recall. If the planet is getting colder, more water is accumulating in ice caps, and there is less energy moving through the cryo/hydro/atmosphere to facilitate evaporation, transport, and precipitation of water. The largest desert on the planet is also the largest store of fresh water on the planet. Condescension does not suit the incorrect, but now you know, and knowing is half the battle!
The other half is violence.