I think somebody's been reading too many articles about Upper Paleolithic Homo sapiens. They probably *were* darker than people in historic times (so there, Jean Auel!), but they had to adapt to the colder and less sunny climate of Europe - especially Northern Europe - and so (like the Neanderthals before them) they started turning out individuals with lighter skin and hair. The correlation between higher latitudes and more lightness is very close.
How long it took, we don't know for sure, but the "European" phenptype (lighter skin and hair, and greater frequency of blue eyes) was pretty well established by the time the Sumerians started keeping track of things going on around them. (And no, no one is sure exactly where the Sumerians came from, but while they were a significan influence on the Near East, they had very little to do with Europe qua Europe.)