About 55.8 million years ago, it got very hot on the earth. During what we call the Paleocene-Eocene Thermal Maximum, average temperatures on earth rose rapidly by about 5 to 9 degrees Celsius (9 to 16 degrees Farenheit). (This event shows up as that narrow spike near the top right corner of the graph.) There is a lot of uncertainty in the estimates because the change in the chemical proxies of temperature is so great, much greater than any other we know of, that we are not sure what it means. Since the world was already warmer than today when this event started, the peak temperature was hot. The warming was concentrated at the poles. The tropics were only a little warmer than today, while the climate in Antarctica was much like it is in Washington, DC today. There was next to no ice on earth, and sea levels were about 150 meters, or 500 feet, higher than today
Nobody knows what caused the warming.
This means a couple of things. First, the earth is subject to rapid and dramatic warming events that we only dimly understand. Second, there does not seem to be any climate "buffer" that would limit warming within a narrow range. So, in theory, the CO2 and methane we are putting in the air now could cause an equally dramatic warming -- although our models show that it would take more CO2 than exists in all the fossil fuels in the world to get such a big temperature increase.
This warming had important effects on life. Many deep sea species went extinct, possibly because of the lack of oxygen in deep waters. On the other hand, it seems to have been a good time for mammals, which increased in numbers and diversity.
The planet is always changing. Some of the changes that come out of the climate models would be very bad for us. But on the other hand, there is no reason to think we would not adapt and go on. The peace and prosperity of the world may be threatened by climate change, but the existence of human civilization is not.