Incomplete understanding of three aspects of the climate system-equilibrium climate sensitivity, rate of ocean heat uptake and historical aerosol forcing-and the physical processes underlying them lead to uncertainties in our assessment of the global-mean temperature evolution in the twenty-first century(1,2). Explorations of these uncertainties have so far relied on scaling approaches(3,4), large ensembles of simplified climate models(1,2), or small ensembles of complex coupled atmosphere-ocean general circulation models(5,6) which under-represent uncertainties in key climate system properties derived from independent sources(7-9). Here we present results from a multi-thousand-member perturbed-physics ensemble of transient coupled atmosphere-ocean general circulation model simulations. We find that model versions that reproduce observed surface temperature changes over the past 50 years show global-mean temperature increases of 1.4-3 K by 2050, relative to 1961-1990, under a mid-range forcing scenario. This range of warming is broadly consistent with the expert assessment provided by the Intergovernmental Panel on Climate Change Fourth Assessment Report(10), but extends towards larger warming than observed in ensembles-of-opportunity(5) typically used for climate impact assessments. From our simulations, we conclude that warming by the middle of the twenty-first century that is stronger than earlier estimates is consistent with recent observed temperature changes and a mid-range no mitigation scenario for greenhouse-gas emissions.