The pessimistic outcome of climate change isn't "wild exponential predictions", though. There are well-understood mechanisms, the margin for temperature increase beyond which modern society collapses is pretty thin, the exponent comes primarily[0] from our economy which has an assumption of exponential growth built-in and will collapse if it suddenly turns into s-curve, and we also have a model of a runaway warming feedback loop as our neighbor in the Solar System.

Also worth remembering is that climate change isn't really about climate. It's about our society. Earth doesn't care about temperature, and life on Earth will happily survive whatever we can possibly throw at it this century. All that matters is that climate change puts pressure on societies around the world, and with enough pressure our entire civilization will collapse, and you and me and everyone else we know will die a horrible death.

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[0] - There are also environmental feedback loops ready to take over the growth of average temperature that have gained attention recently.