We demonstrate that a hemispherically averaged upwelling-diffusion energy-balance climate model (UD/EBM) can emulate the surface air temperature change and sea-level rise due to thermal expansion, predicted by the HadCM2 coupled atmosphere-ocean general circulation model, for various scenarios of anthropogenic radiative forcing over 1860-2100. A climate sensitivity of 2.6 °C is assumed, and a representation of the effect of sea-ice retreat on surface air temperature is required. In an extended experiment, with CO2 concentration held constant at twice the control run value, the HadCM2 effective climate sensitivity is found to increase from about 2.0 °C at the beginning of the integration to 3.85 °C after 900 years. The sea-level rise by this time is almost 1.0 m and the rate of rise fairly steady, implying that the final equilibrium value (the 'commitment') is large. The base UD/EBM can fit the 900-year simulation of surface temperature change and thermal expansion provided that the time-dependent climate sensitivity is specified, but the vertical profile of warming in the ocean is not well reproduced. The main discrepancy is the relatively large mid-depth warming in the HadCM2 ocean, that can be emulated by (1) diagnosing depth-dependent diffusivities that increase through time; (2) diagnosing depth-dependent diffusivities for a pure-diffusion (zero upwelling) model; or (3) diagnosing higher depth-dependent diffusivities that are applied to temperature perturbations only. The latter two models can be run to equilibrium, and with a climate sensitivity of 3.85 °C, they give sea-level rise commitments of 1.7 m and 1.3 m, respectively.