We report on climate projections generated by a simple model of climate change. The model captures the effects of variations in surface solar radiation, using information over the period 1959–2002 available from observational records from the Global Energy Balance Archive (GEBA), as well as increases in greenhouse gases on surface temperature. The model performs well with respect to observational data, and is simple enough to admit a rigorous statistical analysis. This allows us to quantify the uncertainty associated with estimated parameter values using observational data only. Our method immediately leads to estimates with associated confidence intervals, which can be translated into confidence intervals for climate projections. In particular, we construct probabilistic climate projections using standard scenarios for carbon dioxide and sulphur dioxide emissions.