Climate models predict a large range of possible future temperatures for a particular scenario of future emissions of greenhouse gases and other anthropogenic forcings of climate. Given that further warming in coming decades could threaten increasing risks of climatic disruption, it is important to determine whether model projections are consistent with temperature changes already observed. This can be achieved by quantifying the extent to which increases in well mixed greenhouse gases and changes in other anthropogenic and natural forcings have already altered temperature patterns around the globe. Here, for the first time, we combine multiple climate models into a single synthesized estimate of future warming rates consistent with past temperature changes. We show that the observed evolution of near-surface temperatures appears to indicate lower ranges (5-95%) for warming (0.35-0.82 K and 0.45-0.93 K by the 2020s (2020-9) relative to 1986-2005 under the RCP4.5 and 8.5 scenarios respectively) than the equivalent ranges projected by the CMIP5 climate models (0.48-1.00 K and 0.51-1.16 K respectively). Our results indicate that for each RCP the upper end of the range of CMIP5 climate model projections is inconsistent with past warming.