In my experience, temps less that 80F don't really do much for you. Full sun, over 80F puts the fig in the "zone" to ripen with good flavor and good sugars.
A fig will "ripen" at 60F or 70F. It will go through the "motions" of changing color, getting soft, droopy, etc., but will not have the sugars and flavor of a fig ripened at 80-90F. This is why long season figs don't taste good when grown in seasons that are too short. A Panache ripened at the end of September is no where as good as one ripened at the beginning.
Trees on the north side of my E-W driveway all do better than those on the south side. They get more reflected sun and heat.
Can't quote any science or studies or anything else. Have just watched a lot of figs ripen.