To put it bluntly - we (as humans), don't have much use for carbon-fixing products other than burning them and therefore producing more carbon dioxide.
At best, we can hope to become �carbon neutral�
There are two efficient carbon fixers - trees, and carbonate-producing fauna, (corals, foraminifera, ostracods, molluscs, brachiopods etc). (Still with me, poadster?)
Trees, unfortunately have a habit of dying, and returning this carbon to the atmosphere, or when humans 'use' them, unless they form a carbon 'sink'.
If global temperatures continue to rise, the extinction event (assuming that, directly or indirectly, large volumes of the human population are eliminated), will allow vast swathes of tropical / equatorial land to return to its climatic climax vegetation - eg. rain forest.
It may be the case that the elevated temperatures produce new climatic regimes, and the formation of vast, swampy forests.
In this event, the carbon fixed by vegetation may not be returned to the atmosphere when it dies, but may be buried in the swamps, isolating it from the carbon cycle. As these swampy deposits of dead trees build up, more and more carbon is removed from the system (including the atmosphere), forming a carbon sink.
Meanwhile, in the warm seas and oceans, carbonate-fixing fauna will thrive. As they die, they will form carbonate-rich sediments on the sea bed - another carbon sink. The effect will be further enhanced by the fact that the removal of carbon dioxide from the atmosphere will raise the pH of the oceans (ie thy will be less acidic) - this further favours the formation of carbonate-rich deposits.
[cont.]