Why is it that in the last million years during periods of Increased global temperatures it is accepted in paleoclimatology, that the Sahara became green with Savannah and lakes in the African Humid Period, but it is usually said, with the present day anthropologically caused increase in global temperatures, that the Saharah will increase in size and become drier?

It's even stated that part of the reason for increased global temperatures that caused the African Humid period was due to greenhouse gas emissions.

Could it be that Global warming will just lead to wetter climates?