Not in Sahara case. Or to be precise it's cycle of combinations of titling earth axe, changing orbit shape and maybe some other things like solar cycles that all affects global climate all over the planet manifesting among else in Sahara as cycles of desert <> grassland depending on which phase it is ATM.
That solar cycle itself change global avg temperature every few years.
Also around middle age there was "small" ice age. You see, climate seem stable but it isn't even in horizont of hundreds of years. It will change regardless of humans. Point is whether humans help it into good/ neutral / bad phase and how long it takes.

My other point is that eachtime earth was warmer few degrees than today, life boomed.