Much of temperature change of 20th century not correlated with CO2
The rate of temperature rise during the early years of the 20th century was comparable to the current rate of rise, but the level of human contributions to the CO2 was much smaller. Then in the post-war industrial boom when CO2 emissions were higher, the temperature actually dropped significantly.
Current climatologists would see this as no problem to their modeling, since it is projected that the affects of human activity did not produce significant divergence from natural forcings until the post 1970 period. The drop in temperature in the 1940-1965 period is partially modeled in terms of the concentration of sulphate aerosols; those aerosols were reduced after that period.
Collins, et al.