Neandertals and Climate Change

It is now being suggested that Neandertals died out during a marked shift in the earth's climate, specifically the Iberian peninsula. What makes this climate shift different from those that preceded it is that modern humans were on the landscape and could out-compete the Neandertals, so the story goes. It is clear that there was selection for modern genes and that by 25 000 years ago, Neandertals were a thing of the past but I am still with the hybridization crowd.