Extent of desert area influence in local climate
The mediterranian do in a way create its own climate and is partly protected from the north saharan desert by the dominating wind direction in the area.

The dominating wind direction is from west and northwest,The wind blows into the saharan desert in the direction of the equator in the winter,This creates the mild winters the mediterranian is known for.

In the summer more warm and dry air moves from the north saharan desert and into the mediterranian area,this creates the dry summer climate the mediterranan is known for.

So the north saharan desert have the strongest influence on the mediterranian climate in the summer.

you can read about it here https://en.wikipedia.org/wiki/Hadley_cell if you click on the animation you can see how the precipitation changes over the year and thereby also the temparature.

and here https://en.wikipedia.org/wiki/Mediterranean_climate