The research was led by Professor Chronis Tzedakis, a palaeoecologist at the University of Leeds, who explained: �Until now, there have been three limitations to understanding the role of climate in the Neanderthal extinction: uncertainty over the exact timing of their disappearance; uncertainties in converting radiocarbon dates to actual calendar years; and the chronological imprecision of the ancient climate record.�
The team�s novel method � mapping radiocarbon dates of interest directly onto a well-dated palaeoclimate archive � circumvented the last two problems, providing a much more detailed picture of the climate at the possible times of the Neanderthal disappearance.
More here. The upshot is that they looked at three dates for the disappearance of Neanders, and none of them corresponded to dates of climatic instability or rapid change. It's only in one site, however.