The Earth's climate reconstructed over 4.5 million years. The temperature was around 3°C higher for a comparable CO2 concentration in the air.
The researchers used many indirect measurements of temperature. They used the concentration of two oxygen isotopes found in fossils of foraminifera, widespread microorganisms with carbonate shells that lived on the ocean floor. This made it possible to deduce the temperature of the seabed, then that of the ocean surface, and finally the average temperature on Earth.