That was my first thought too. But it seems like extinction isn’t likely. To a first approximation, if the human population really was decimated by climate change to the point where there were only a few surviving settlements, there wouldn’t be industrial level emissions any more, and carbon dioxide levels would start to go down.
There are a couple complications that make that story I told inadequate: temperature inertia from the oceans and a runaway greenhouse effect. Oceans that have already been warming will continue to heat the atmosphere even if emissions stopped today; best estimates suggest it would raise atmospheric temperatures by about 0.55˚C.1 This is not nothing, but neither is it an extinction level threat. A runaway greenhouse effect is what is hypothesized to have happened on Venus. Water vapor is a greenhouse gas, and as the planet warms, there is more water vapor in the air, resulting in a positive feedback loop. On Venus, so the hypothesis goes, this caused the oceans to boil off. The scientific community has concluded, thank God, that this will not happen on earth. Even the more concerned scientists say that a runaway greenhouse effect could only result if we released 10 times the amount of carbon dioxide that would come from burning all the oil, coal, and natural gas in the earth’s crust.2 Also, the model doesn’t take into account the fact that if the water vapor forms clouds, it cools the earth instead of warming it.
Having addressed those complications, I think it is reasonable to conclude that extinction is extraordinarily unlikely from climate change. Another cause for comfort: there are some relatively simple geo-engineering techniques that could temporarily cool the planet down pretty fast. If you explode enough things, all the dust in the air would cool things off nicely. Krakatoa did this.3
Don’t get me wrong. Climate change is going to suck. It could very well happen that the world population gets cut in half until there simply isn’t as much demand for fossil fuels. But extinction would be many orders of magnitude worse. We can recover from decimation. We cannot recover from extinction.