Also, here's a list at some of the dramatic swings in temperature and sea levels over just the past 2 million years, including many events impacting modern human history, such as the Little ice age: http://www.physicalgeography.net/fundamentals/7x.html
Which is normally what happens after a civilisation crash.
Getting back to the level of the Middle Ages is fairly easy to do - many, many people can figure out some of the basics even from first principles. Figure out a windmill, weaving, fulling, irrigation etc just from the basics people got going through school probably in just a few years.
Yet the more advanced tech? That's a system fragility. Easy to lose, hard to get back if lost. If there's mass destruction of cities, relocations, perhaps wars and huge numbers of deaths and displaced people why expect a globalised, technological and mainly online world to survive?
Could just as easily find ourselves in the same boat as those in the worlds after the Romans, Greeks, Egyptians etc. Lots of things we can see but have no idea how to recreate. It could take hundreds of years to claw our way back to creating chips. Once the first generation that remembers high school or uni is passed, it gets even harder...
It doesn't look like we had such rapid warming before, at least not in the last million years where we have decent data. We don't know how the ecosystem will handle it.
New Zealand was the same. Humans arrived around 1300 and we lost the moa and Haarst's eagle (the world's largest flying bird) by around 1400.
Incidentally, the largest species of bird that ever lived was the elephant bird of Madagascar. It weighed up to 730kg (1600lbs) and stood 3m (10ft) tall. It went extinct around the year 1200.
There used to be a lot more interesting animals around, but our ancestors hunted them to extinction. Nobody misses them because nobody alive today ever had them in the first place.
It's sad, but even the extinctions of the coolest, most amazing creatures are quickly forgotten. When the giraffe or blue whale is gone, it will just be another story like the elephant bird.
Setting aside snide remarks, the concern most people have for the environment is not about "life", it is about our civilization. We have seen huge advances in quality of life in the past 100 years, because of increases in medicine, trade, and mobility. These characteristics rely on a relatively peaceful coexistence across the globe.
The fear is that increased survival pressure will void most of those advances. If global trade breaks down, we might lose the technology and infrastructure that enables us to feed 7+ billion people. So regardless of whether the Earth's climate will kick us out, we still might end up returning to population levels of the 1900s.