Neanderthals and Extinction

So a brief period of rapid cooling in Europe may have done in the Neanderthals.  Good news is that nothing like that could happen to modern humans.  Right?

"Studying Neanderthal behavior is an opportunity to understand how a rapidly changing climate affected our closest human relatives in the past. If Neanderthal populations were already on the edge of survival at the end of the Ice Age, the increased competition that occurred when modern humans appeared on the scene may have pushed them over the edge."

Increased competition while the Neanderthals were struggling with the impact of the Campanian Ignimbrite eruption in Italy.  This was a massive volcanic event that led to a short period of reduced temperature in Europe.  Although considered an unlikely primary cause of the Neanderthal extinction, the reduced temperatures may have been the tipping point for the Neanderthals who were under great stress from modern humans.

...the abrupt cold spell that followed the eruption would still have significantly impacted day-to-day life for Neanderthals and early humans in Europe. Black and colleagues point out that temperatures in Western Europe would have decreased by an average of 2 to 4 degrees Celsius during the year following the eruption. These unusual conditions, they write, may have directly influenced survival and day-to-day life for Neanderthals and anatomically modern humans alike, and emphasize the resilience of anatomically modern humans in the face of abrupt and adverse changes in the environment.

Thought experiment...What would happen to life on the planet if you increased the mean temperature by 2 to 4 degrees Celsius?