This publication analysis a correlation between the cumulative CO2 emissions and the global surface temperature change.
The change in global surface temperature was calculated as the difference in the two most recent 31 years neighboring periods, and the change in the cumulative CO2 emissions is the difference between the actual values in the centers of the periods.
This approach resulted in 0.000556°C/GtCO2 for the year 2000 and 0.000745°C/GtCO2 for the year 2021.