So what happens to the indigenous population of animals (polar bears are the first that come to my mind) when this happens? Do they just die out or are there groups trying to get them to safety?
We have already seen many, many species go extinct. The exact figures are not well understood, but there's a lot more at stake than just the polar bear. https://en.wikipedia.org/wiki/Holocene_extinction
There's a 2009 paper "Planetary Boundaries: Exploring the Safe Operating Space for Humanity" that may be of interest.
> The planetary boundary (PB) concept, introduced in 2009, aimed to define the environmental limits within which humanity can safely operate. This approach has proved influential in global sustainability policy development. Steffen et al. provide an updated and extended analysis of the PB framework. Of the original nine proposed boundaries, they identify three (including climate change) that might push the Earth system into a new state if crossed and that also have a pervasive influence on the remaining boundaries. They also develop the PB framework so that it can be applied usefully in a regional context.
edit: and the indicator that is off the charts relative to its corresponding "safe operating space" boundary is biodiversity loss - measured in species extinction/(millions of species * year). Climate change looks practically controlled compared to that. (ha).
