It could actually be pretty fast. For example if the Gulf Stream current stops from all the ice melt. Or when the methane all boils out of the artic tundra. Then areas near the equator near sea level could simply be uninhabitable for most mammals. They would have to move North or South, or change elevation. There is a lot of pretty unoccupied land in Northern Siberia, Canada, and Southern South America. Right now, those places are too cold for almost everybody. After we warm up a lot, the Inuit will have to learn agriculture. The Mayans can teach them to grow corn and chile peppers.