What is the unit impact of $\small\sf{CO_2}$ on global temperature?

I'm trying to find the impact of X tonnes of CO2 on global temperature so I can infer the unit impact of CO2 on temperature. While we know there is a positive correlation, I can't seem to find a study that provides a coefficient.

Any guidance would be helpful.

$${\displaystyle \Delta F=5.35\times \ln {C \over C_{0}}~~(\mathrm {W} ~\mathrm {m} ^{-2})\,}$$
• If my calculus hasn't deserted me after all these years, I think that (taking the derivative), along with the "commonly accepted value of climate sensitivity parameter λ, 0.8 K /(W m−2)" (your Wikipedia link), leads to a resulting approximation that a 1 ppm increase = a $4.28/C$ Celsius change in temperature, so at around the current 415 ppm, that's 4.28/415 ≈ roughly a 0.01 °C per ppm increase... which seems to make sense a very very rough value to me? So hopefully that finishes the idea to fullness for the question's focus about the unit increase. Mar 1 at 3:33