Projections of 21st century warming may be derived by using regression-based methods to scale a model's projected warming up or down according to whether it under- or over-predicts the response to anthropogenic forcings over the historical period. Here we apply such a method using near surface air temperature observations over the 1851–2010 period, historical simulations of the response to changing greenhouse gases, aerosols and natural forcings, and simulations of future climate change under the Representative Concentration Pathways from the second generation Canadian Earth System Model (CanESM2). Consistent with previous studies, we detect the influence of greenhouse gases, aerosols and natural forcings in the observed temperature record. Our estimate of greenhouse-gas-attributable warming is lower than that derived using only 1900–1999 observations. Our analysis also leads to a relatively low and tightly-constrained estimate of Transient Climate Response of 1.3–1.8°C, and relatively low projections of 21st-century warming under the Representative Concentration Pathways. Repeating our attribution analysis with a second model (CNRM-CM5) gives consistent results, albeit with somewhat larger uncertainties.