Iguana, the reason why the out of africa is quasi-creationist is because it tries to claim a common ancestor for all humans that is far too recent. There was that bizarre, "african eve" claim for example, which clearly was an attempt to fashion a quasi-Biblical "adam-and-eve" type story to human evolution. The Out of africa theory is also quasi-creationist since its proponents have been trying to claim falsely, for decades, that modern humans are not descended from apemen nor interbred with them, yet current evidence shows that modern humans share DNA with at least 2 apemen types, with indications of other types of apemen DNA being present as well. So it seems that our DNA came from all over the "Old World" not just Africa.
Then there's the overly simplistic diagram you showed. For example, some evidence has come to light, suggesting that modern East Asians may be partially descended from advanced types of homo erectus. So the old, silly notion that Neanderthals and Homo Erectus were "behind" modern humans, in an evolutionary sense, must be wrong. And that silly notion was directly derived from the Out of Africa theory which wrongly claimed, for decades, that Neanderthals and Homo Erectus were so stupid, lacking culture or the ability to talk that it was supposedly impossible for modern humans to have interbred with them. Now that various different kinds of "apeman" DNA have been found in modern humans and more evidence has come to light showing that Neanderthals etc. were on a par with modern humans, the OA theory is increasingly showing flaws.
Ok, I read a bit on this subject (various articles on Wikipedia and for example this page
http://www.actionbioscience.org/evolution/johanson.html explaining both theories and this one
http://www.sciencedaily.com/releases/2011/07/110718085329.htm which comes to an opposite conclusion) and now I understand better what you mean. I had the wrong idea that the so called “Out of Africa” theory was about the global origin of both sub-species, Sapiens and Neanderthals, thus I didn’t understand because Neanderthals are also supposed of African origin:
Neanderthals, whose ancestors left Africa about 400,000 to 800,000 years ago, evolved in what is now mainly France, Spain, Germany and Russia, and are thought to have lived until about 30,000 years ago. Meanwhile, early modern humans left Africa about 80,000 to 50,000 years ago. The question on everyone's mind has always been whether the physically stronger Neanderthals, who possessed the gene for language and may have played the flute, were a separate species or could have interbred with modern humans. The answer is yes, the two lived in close association. (from 2nd link above)
But, according to what I read elsewhere, modern humans carry no more than a very small amount of Neanderthal genes in their DNA (1 to 4%, as I mentioned before) - or none at all as is doubtlessly the case of Africans.
I feel that both theories are neither necessarily incompatible nor conflicting in a binary way, because they are neither dogmatically rigid nor monolithic.
Anyway, as Neanderthals have their origin in Africa too, what is the argument? They had populated Europe for a longer period of time and thus should have been better adapted to cold climate, I suppose? Ok, but what does it change if 3 generations only suffice for an adaptation to the cold, as you wrote?
The issue of adaptation is simple:- we would only need 3 generations or so for most people to adapt to the cold, with quite a number now already adapted, provided they ate raw foods like the Inuit and understood simple survival tips like living in igloos or survival shelters in the snow etc.
So, is the issue about some interbreeding or no interbreeding at all between Sapiens and Neanderthals relevant concerning resistance to cold? Who cares, except anthropologists?
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