Based on a comparison with Upper Paleolithic sites in Europe we see an overlap in the ages of Châtelperronian industries and Aurignacian lithic assemblages . . . which is consistent with an acculturation at distance model for these late Neanderthals. The Proto and Early Aurignacian appear contemporaneous indicating that this transition was rapid in this region.
From Sahra Talamo et al., "A Radiocarbon chronology for the complete Middle to Upper Palaeolithic transitional sequence of Les Cottés (France)" Journal of Archaeological Science doi:10.1016/j.jas.2011.09.019 via Dienekes Anthropology blog.
The onset of an ice age didn't do the Neanderthals any favors and certainly contributed to their inability to hold back an advancing wave of modern humans with more sophisticated stone tools, although the extent to which Neanderthals died off leaving vacant territory, were outcompeted for resources by incoming modern humans, were absorbed into the modern human population, or were actively killed by modern humans is less than clear. A one thousand year gap surely does not suggest closely integrated populations.
From the comments to that post:
41,000-39,000 y.a. (possibly corresponding in age to the Heinrich event H4?), a relatively cold phase (a Heinrich event) during the 'middling' period ago (Oxygen Isotope Stage 3)... Huijzer & Isarin (1997) have summarized the general climatic and ecological conditions for north-western and central Europe for this phase, based on a range of indicators including plant fossils, insect fossils, ancient dune features and permafrost features. . . . to the south of a large ice sheet (approximately following the southern limits of present-day Norway and Sweden), there would have been arid conditions with sparse vegetation cover, with aeolian sand sheets active, and some loess (windblown dust) deposition in areas where at least some vegetation was present.
Mean annual temperature was similar to the high Arctic of the present-day; around -9 to -4 deg C, and the mean temperature of the warmest month across north-west Europe was around 10-11 deg C; equivalent to the tundra zones today. The coldest month would have varied from around -27 to -20 deg C from north (Denmark) to south (northern France).
This interval, correlated with a Heinrich event or ice surge in the north Atlantic, was one of the intense cold and dry stages of the last 100,000 years in western Europe, though it is uncertain whether this cooling extended much outside of Europe (unlike the glacial maxima which seem to have been fairly global in their extreme conditions).
There is no sign that modern humans ever made it into Europe proper before this point. There are considerably earlier indications of modern humans in the Levant and South Asia, at least, and perhaps Southeast Asia and China as well, in parts of the period from 100,000 years ago to 50,000 years ago. The expansion of modern humans into Europe, once it started, appears to have been rather swift, perhaps just two or three thousand years for these hunter-gatherer Cro-Magnon modern humans. Archaic humans may have had a sufficiently health society to keep modern humans at bay until the ice age climate swing crippled their ability to cope.
Of course, once the ice age associated with the Middle to Upper Paleolithic transition was long gone and esssentially all archaic hominins had gone extinct, the ice age associated with the Last Global Maximum struck around 20,000 years ago, forcing a retreat from much of Europe and a lowering of the sea level, followed by a repopulation of Europe and the colonization of the Americas by modern humans (the first hominin species to arrive there).
UPDATE (October 7, 2011):Maju provides some helpful links that provide information that expands the on this post in the comments. Based on that material I add this update.
The paleoclimatic conditions that triggered the onset of the transition from Neanderthals to modern humans in Europe appears to have been triggered by the biggest volcanic erruption in the Mediterranean area in modern human history, which took place 39,300 years before present, essentially contemporaneous with the transition time seen in Southwest France.
The abstract of a 2002 paper by Fidele, et al, (paragraph breaks added for readability in blog format) notes that:
The Campanian Ignimbrite (CI) eruption (Phlegraean Fields Caldera) was the largest volcanic eruption in the Greater Mediterranean area over the past 200 Ka (at least 150 km3 DRE). Ash layers correlated with CI have been found in sediments of the eastern Mediterranean Sea (Y5) and East Europe, from Italy to the former USSR.
The recent dating of the CI eruption at 39.3 Ka BP draws attention to the coincidence between this volcanic catastrophe and . . . the European Late Pleistocene shift (ELPS). . . . our investigations show that:
(1) at several archaeological sites of peninsular Italy a distinct tephra layer corresponding to the CI is regularly interbedded between the last documented Middle Palaeolithic and the earliest appearance of unquestionable Upper Palaeolithic assemblages;
(2) at the same sites the CI tephra coincides with a interruption of occupation, several millennia long;
(3) in the GISP2 Greenland ice-core, Lago Grande di Monticchio (southern Italy) lacustrine sequences, and KET 8003 Tyrrhenian sea-core, a large volcanogenic sulfate signal (375 ppb, at 40,062 yr BP) to be correlated with the CI eruption and/or CI tephra layer occurs just before a sharp climatic shift which coincides with the onset of Heinrich event 4 (HE4). The concurrence of the CI eruption, Palaeolithic site abandonment and beginning of HE4 suggests that the overlapping of CI eruption and HE4 climatic impacts induced ecosystem crisis on a fairly large scale - human systems included - and well beyond the direct-impact zone. Moreover, the occurrence of the CI eruption just before HE4 probably corroborates the positive climate-volcanism feedback supposed for other high magnitude eruptions (e.g. Toba, 74 Ka).
The study itself doesn't take the extra step of claiming that the coincidence in time amounts to proof that the Neanderthal to modern human transition was caused (at least in terms of the specific time at which it happened) by this huge volcanic erruption. But, this event's scope, magnitude, and close coincidence in time with the transition makes it clear that it played a pivotal role in that event.
Yes, Neanderthals had suffered previous ice ages during the period when they were found in Europe. But, it isn't at all clear that the previous ice ages, while perhaps just as severe, had such a violent and sudden onset. It is also the case, of course, that on previous occasions, that there was not another hominin species as strongly competitive as modern humans to step into the breach.
When modern humans began to make inroads into Europe, it took place at a time when, it is fair to assume, Neanderthal population numbers were impaired from a baseline which was probably never very large (estimates from the diversity in ancient Neanderthal DNA are on the order of 4,500 which is a decent fit to the density one would expect for a top of the food chain predator of their size with a range similar in size to theirs), when the traditional lifestyle was less functional than it had been in the recent past and their own state of health may have been impaired by the meager resources available following this volcanic erruption triggered ice age.