CO2 levels have not doubled. They have risen from about 285ppm to 386ppm.
That equates to 0.44 of a doubling (=LOG((386/285),2)-1).
Climate sensitivity over the long term to CO2 doubling is more likely about 3C/doubling.
So, we expect about 1.3C of warmth from the rise in CO2.
However, there has been a increase in cloudiness over the last century from sulfate aerosals
that has resulted in about 0.5C of cooling.
The total temperature increase from 1850-1899 to 2001-2005 is 0.76°C ± 0.19°C.