Nix, there are so many holes in your science that it is difficult to know where to start.
Firstly, you're ignoring population migration. Species do not simply stay in one place and die out. Population trends amongst species often demonstrate that they follow the movement of their specific climatic bands. For example, seasonal migration.
In your own very narrow example, you're citing a regional "extinction" rather than a species-wide issue - in which case, it is the narrowing of a given climatic niche at issue, not the geographically local fluctuations.
Secondly, you are generally ignoring the fluidic nature of the relationship of and between both fauna and fauna, and their place within inter-related ecosystems.
Thirdly, you are making sweeping assumptions regarding the North Atlantic Drift, and completely ignoring its place within global oceanic currents. It is not a stand-alone mechanism, subject to the effect of temperature alone. It takes great influence from other factors, such as energy gradients, oxygen content, salinity, landmass deviations, inherent pressures, etc.
Fourthly, your assumptions regarding the adaptability of life to natural climate change are clearly erroneous. If you are correct, and "global warming" is indeed a man-made factor in the current climatic cooling trend, then logically it follows that this ought to be the beginning of the first mass extinction event. Why? Because, by your reasoning, life would adapt to natural environmental changes and fail to survive human-created ones.
This is clearly an erroneous assumption. Flood Bassalt Events, for one, have been a major cause of extinctions. Indeed, the most severe extinction event - the Permian-Triassic - was of this nature. Go look it up.
Fifthly, you sre ignoring entirely vast swathes of information which contradict your assumptive "fact" base. Notable theories with much factual basis include global dimming effects, oceanic saturation, solar-climatic interactions, and so on. Man-made "global warming" is but one possible extrapolation of current observations.
But, much like the plumb-pudding model of the atom back in 1904, it fails to explain many of the finer points within its supposedly logical framework. Or, worse, trips over its own logical toes.
Such as;
Yearly natural CO2 emission is greater than human contributions over the past 150 years.
Radical temperature spikes contrary to theoretical precedent offered by "global warming" theory.
Global dimming contributions.
Solar luminosity fluctuations.
Heightened late 19th/early 20th century vulcanism.
The list does go on.
Lastly, though, you are fulfilling the radical environmentalist stereotype. You pursue an agenda without fully grasping basic and fundamental concepts, arguing your case with a disturbingly religious vigour. In seeking to enforce your beliefs you are completely missing out on the important facts.
Nature is change. Science is hypothesis and theorem supported by fact.
Presumption is a most dangerous mistress.