I would argue that the species will be fine. If your definition of 'fine' is the species surviving. If 99% of the human race were wiped out by Global Warming we would still have 70 million humans on the planet (approx one UK). That should be more than enough to repopulate given a long long time.

Obviously that would be a terrible disaster the likes of which our race has never seen. 100 times the death toll of WW2 and would destroy pretty much all our infrastructure etc as supply chains fail etc. This is something we should strive to avoid at all costs but I do think the species would survive. We are quite a hardy bunch actually.