You know enough to be dangerous. Yes biodiversity was higher in the distance past when the Earth was warmer, but even more telling is what happened in the distant past when the Earth warmed at a very fast rate. The Permian–Triassic extinction was likely caused by an approximately 10 degree warming event that took place over tens of thousands of years. That lead to the extinction of almost all life on Earth. The current warming trend that the Earth is in is much faster than the trend associated with the Permian-Triassic extinction, and the obvious concern should be that this will lead to an even larger extinction event than the Permian-Triassic extinction. Plants can only migrate at a certain rate. Similarly for animals. Most won't be able to adapt, causing ecosystem failures. Maybe 99.9% of life will go extinct, who knows. Let's just dive right in!
Random fact: You can easily spot the Permian-Triassic sediment deposits because there are two layers: (i) the Permian layer is loaded with fossils, and (ii) the next layer has only sand stone. Why? When almost all of the plants and animals die, all that is left is a giant dust bowl.