Were the Neanderthals wiped out by the cold?

> " rather than being Neanderthal killers, the original human settlers of Europe almost suffered the same fate".

I don't know about the theory in the article;
but this phrase is wrong. It implies that Neanderthals (Homo Sapiens Neanderthalensis) were not human - but they were. They had fire, they crafted tools and ornaments, they buried their dead ritualistically; their brain was somewhat larger than that of modern humans. Their numbers were never very large, and for some reason they failed to survive the last cold spell - but it remains true that they survived previous ones, thanks to their effective technology.

I believe the latest theory for the extinction of the Neaderthals is that they had poorer anatomy for speech and would have had a limited range of language sounds.

I have heard another theory. That the Neanderthals died because they were carnivores, with higher caloric requirements to survive. Then their main meat supply (megafauna like mammoths) went basically extinct around the time the last ice age ended.

Lots of muscle mass and a large brain do not help you survive when you cannot support them. Our bodies are quite energy efficient, I suspect more efficient than those of the Neanderthals. Muscle tissue has a high energy maintenance requirement. Our bodies tend to eliminate unnecessary muscular mass, in order to lower our energy requirements (with the side effect of muscle wasting on astronauts in zero-g).