A multiple linear regression analysis of global annual mean near‐surface air temperature (1900–2012) using the known radiative forcing and the El Niño–Southern Oscillation index as explanatory variables account for 89% of the observed temperature variance. When the Atlantic Multidecadal Oscillation (AMO) index is added to the set of explanatory variables, the fraction of accounted for temperature variance increases to 94%. The anthropogenic effects account for about two thirds of the post‐1975 global warming with one third being due to the positive phase of the AMO. In comparison, the Coupled Models Intercomparison Project Phase 5 (CMIP5) ensemble mean accounts for 87% of the observed global mean temperature variance. Some of the CMIP5 models mimic the AMO‐like oscillation by a strong aerosol effect. These models simulate the twentieth century AMO‐like cycle with correct timing in each individual simulation. An inverse structural analysis suggests that these models generally overestimate the greenhouse gases‐induced warming, which is then compensated by an overestimate of anthropogenic aerosol cooling.