In this version, it was cold, not heat:
Now, an extensive modeling study based on paleoclimatic data and nearly 3,000 archaeological records suggests that global cooling episodes were a major driver of the extinction of the Neanderthals as well as the long-gone Homo species H. erectus and H. heidelbergensis. To the authors of the research—published today (October 15) in One Earth—the findings are an ominous warning from the past with regard to our own future in a rapidly warming climate. But some other experts note that the fossil record isn’t reliable enough to draw such conclusions about past hominin extinctions with certainty…
The team compared that to the environmental conditions the species were experiencing at particular timepoints. Those comparisons suggested that for three species—neanderthalensis, erectus, and heidelbergensis—their climatic niches appeared to suddenly contract just before their last known appearance in the fossil record.
Katarina Zimmer, “Climate Change Helped Drive Homo sapiens’ Cousins Extinct: Study” at The Scientist
So these explanations will have to move over:
In other words, all we really know for sure is that, as a distinct human type, Neanderthals died out. There is a bonanza of speculation as to why that happened. Some say current humans crowded them out. Others say it was due to interbreeding with current humans (of course, for a minority group, that is a form of crowding out, just not necessarily a violent one). Alternatively, they died before we even got there. Or succumbed to an early industrial revolution. But according to one account, Neanderthals kept us alive precisely because we inherited some of their genes, not that it did them much good.
Some researchers look for physiological clues. Neanderthals tended to have shorter lower legs than modern humans, which helped them move more efficiently in the hills.” But, others point out, they had weaker Achilles tendons, and therefore inferior running ability, which “hits at the crux of why Neanderthals went extinct.” According to some, their large eyes caused their demise (because “more of their brains were devoted to seeing in the long, dark nights in Europe, at the expense of high-level processing”). Apparently, they hung on a while in the Polar Urals in northern Russia. But we really don’t know for sure what happened to them.
Denyse O’Leary, Neanderthal Man: The Long-Lost Relative Turns Up Again, This Time with Documents, Evolution News and Views
Eventually, there will be more explanations for the demise of the Neanderthals as a separate group than there were Neanderthals. But never mind, the series has plenty of episodes to run in the meantime.