Whilst doing some further reading, I found this article by Crowley and North that discussed climate variations and its relation to extinction. Instead of posing obvious connections between climate change and extinction, they mentioned that the magnitude of Late Permian extinction seemed to be too great for the area of land to be affected by glaciation. Also, there was no major extinction event during the Late Carboniferous (330 Ma) glaciations, but a significant reduction in some faunal groups. Certainly, some evidence for the three of five extinction events shows connection to the evolution of Cenozoic climate at about 2.4 to 3.0 Ma.
An interesting fact - climate change does have an impact on extinction. Many extinctions occurred at the early stages of cooling millions years ago, with each cooling event removing the most vulnerable species. As species that are more adaptive remained, the effect of climate change on extinction has been smaller since then.
At least, one of the mass extinctions - the Mid-Jurassic, was argued to be triggered by massive climate change, a mega monsoon. Dr Ruben Cuneo explained the possibility on BBC.
Fuelled by my personal interest on animals, I spent some time to look up some endangered species on WWF's website.
Worryingly, these marine turtles are only the tip of the iceberg of endangered species in the world..