No, it won’t, and the belief that climate change will lead to human extinction is not a useful one. For most of earth’s complex multicellular life history, it was much hotter than it is right now or even than most projections have it becoming; for most of it, there was no permanent ice anywhere on Earth. During the Cretaceous, the Earth was a whopping 10 degrees Celsius hotter than it is right now, which is way, way more than climate models project. Life on earth is extremely capable of surviving and thriving in vastly hotter temperatures than we are capable of producing.

The problem is not the end result, but the period of transition - mass extinction in the biosphere and massive, dramatic collapse of current ways of human life in big swathes of the world. Places like Canada or Russia will become much more habitable to humans, but the process of changing human society and relocating huge numbers of people (especially when taking a realistic, materialist look at social and economic systems) reveals how utterly devastating climate change will be.