The basic radiative physics which describes CO2 as a greenhouse gas is well accepted by nearly all the scientific community. To within a well confined margin for error, the Planck Temperature Response for a doubling of CO2 in Earth currently constituted atmosphere is ~1.2K. The uncertainty, therefore, with regard to the direct impact of CO2 on global temperature is very small.
If we doubled CO2 we could expect at radiative equilibrium, a temperature rise of 1.2C. No one would claim that to be a major problem. It would entail some adaptation, there would be winner and losers, but the consequences to the ecology and human condition would remain manageable.
1.2C is not the end of the story however. If the climate system were such that nothing else changed in response to a 1.2C warming we would know for relative certain what to expect from a global warming due to an increase in atmospheric CO2. The climate system is sensitive to a change in temperature however. The entire system will respond to a change in average temperature, such that local, regional and global climates will be affected.
Atmospheric water vapor will increase. Cloudiness, will likely increase. Ice will melt. Sea levels will rise. Vegetation and animals will migrate to keep up with shifting climate zones. Grass land becomes desert. Desert shifts to grass land. Grass land shifts to scrub brush and then forests. The global water cycle is affected. Precipitation patterns are altered. Jet streams migrate. etc.
So just how sensitive is the climate to a gradually changing temperature perturbation which becomes in isolation 1.2C at equilibrium? Many estimates, and varied approaches have been applied to arrive at a general range of 2C-4.5C. This is the so called Charney Sensitivity understood since the 1970s and adopted by the IPPC AR4 for it's 2007 report.
Can we do better than that wide range of probability to the 95% confidence level? The Charney Range represents a whole world of difference in outcome from one end to the other.
https://www.carbonbrief.org/explainer-how-scientists-estimate-climate-sensitivity
https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/climatsensitivity.html
