No one is claiming humanity will go extinct. But during that ice age there were probably less than 100k living in the whole world. With technology and our current spread, we won't go so low, but a planet 3-4 degrees hotter is nowhere near able to sustain 7B people. Not to mention the terrible migration and resource wars we'll see as hundreds of millions if not billions of people have to leave places where temperatures routinely rise over livable standards.