There are lots of Neanderthal skeletons, but almost nothing to show that people were actually living where the bones were found. It is as if some people had wandered out of their comfort zones, and died in those harsh places, like the case of Ötzi the Iceman. 

If Neanderthals were living in the cold interior areas of Eurasia for a few hundred thousand years, why is there so little evidence of hunting weapons, and fire for warmth, and charred bones from cooking? Maybe those people were just visiting those places, like the Vikings who visited England, and the humans who visited the Moon. They didn't actually live there.

I think Neanderthals were living for hundreds of thousands of years on Bioko, without inventing tools, weapons, or fire. Those who left Bioko, migrated along the continental margins of Africa and Eurasia. Those Pleistocene coastal areas are now submerged and any traces of those people are hidden.

Neanderthals who came to Eurasia may have lived mostly along the shore of the relatively warm Mediterranean Sea. The water was much colder than Bioko, but swimmable. They lived mostly on marine foods. Proof that Neanderthals commonly swam in cold water is seen in many of their skeletons: Neanderthal skulls show exostoses ("surfer's ear") — typical in humans who spend a lot of time in cold water.

Some Neanderthals must have wandered into interior parts of Europe during the warm summer season when they could find forest foods. Some of them died in those cold places, leaving fossil skeletons. Those were not such good places to live, but good places to die. Neanderthals in Europe were probably living on the edge.

It's a model. We can see if it works. 

To learn more about the earliest DNA, and what it tells us about Denisovans, Neanderthals, and Sapiens, read this article in Nature by Meyer et al. (2014)