1. First, you are correct, the Earth was much hotter in the past, and I haven't seen anything convincing that global warming will lead to a fundamental "runaway greenhouse" effect a la Venus that makes life as we know it on Earth unsustainable.
2. That said, a huge climate change in a relatively short amount of time could easily lead the the deaths of billions of people, with a B. One third of the human population lives within 60 miles of the coast. Rising temperatures will lead to huge portions of the planet that are currently densely populated that will no longer support humans. The resulting migrations, "resource wars", and overall increase in extreme weather events (more hurricanes, more droughts, more floods) will lead to death and misery to a huge portion of humanity.