This is precisely why Dr. Guy McPherson has predicted human extinction on earth by 2030. Methane clathrates coming from the Arctic sea floor and from Canadian and Siberian permafrost. This is the most serious threat we face now.
Not that it would be easy or desirable. Some of the worst scenarios might result in 99% (or higher) of humans dying - obviously an unspeakably immense tragedy. Yet that would still leave tens of millions of people to carry on.
It seems to me that it would be extremely difficult to extinguish human life entirely, given our cleverness, adaptability, and very strong survival drive.
I haven't seen much talk about projections that would make the entire planet completely uninhabitable for humans. That would require an increase significantly higher than 10° Celsius, I'm guessing?
Of course, this would likely delay our transformation into a space-faring civilization by a few thousand years, as well as significantly damage social progress.
However, there's a very important distinction here: The permian triassic boundary conditions did not arise coming abruptly out of an ice age. An ice age after a warm period leads to lots of methane being stored, and it's reasonable to assume that the current methane storage is much larger than at the permian triassic (oh, did I mention that that was already an extinction event, probably the worst we know about?).
All in all it's not completely out of the question that an abrupt release of enough methane could lead to a Venus syndrome, and thus the complete sterilisation of the planet.
Probably not. That amount of increase will likely disrupt every food chain on the planet, and larger lifeforms will not be able to adapt fast enough. That means extinction time for everything larger than a mouse or unable to migrate.
Even if some arable land remains around the poles, the most you will find growing there is moss and grasses. Wheats require a very rich soil, which will either not be there or be exhausted after a few crops.
In order for the south pole to be the best place to live all the ice would have to melt, which would essentially end life on earth as we know it. The sea level would rise about 100m, which would kill so much life on land that it would make the atmosphere unbreathable and kill everything else.
More fundamentally if we can't get it together enough to stop this, I find it highly unlikely we'll be able to put together a self-sustaining shelter on what will basically become an alien planet. We'd have to survive indoors for the length of our written history, minimum. It's not so much that it's outright impossible, but any tiny problem could lead to our extinction over ten thousand years. It's a lottery ticket for our species, and the only realistic expectation is that we will lose.
Plus there are tons of survival-killers that just get discounted. Will we be able to keep ourselves going technologically without a global distribution of resources? Will our genetic diversity survive isolation? Will we be able to survive antibiotic-resistant diseases?
We're struggling to stay ahead of antibiotic resistance with decades of mutation- once we no longer have the scientific effort to devote to controlling this, will we be able to do anything about centuries or millenia of bacterial evolution? A freak drift or reservoir incident (eg ebola in bats) could wipe us out in a week or two.
This could cause a global asphyxiation event.
Reference. https://cosmosmagazine.com/palaeontology/big-five-extinction...