This chart isn't the easiest to understand...Usually timelines put older stuff on the left and newer stuff on the right, and this one has it reversed. The farther you go to the right, the farther into the past you get. But the chart shows a link between CO2 and temperature, but has no implication for cause and effect. However, saying that CO2 is an effect of heating and cooling doesn't explain what the source of the CO2 is, since matter has to come from somewhere.
Obviously, since humans weren't producing shit tons of CO2 tens of thousands of years ago, we can only say that natural processes dictated the temperature. Nothing was putting more CO2 in the air, only the temperature was changing vis a vis the aforementioned variables that I've mentioned. As the temperature gets hotter, the ocean releases CO2, and CO2 levels go up. So just one of the places where CO2 is an effect, not a cause.