Extensive covers of supraglacial debris are often present in glacier ablation areas, and it is essential to assess exactly how the debris affects glacier melt rates. This paper presents a physically based energy-balance model for the surface of a debris-covered glacier. The model is driven by meteorological variables, and was developed using data collected at Miage glacier, Italy, during the ablation seasons of 2005, 2006 and 2007. The debris surface temperature is numerically estimated by considering the balance of heat fluxes at the air/debris interface, and heat conduction through the debris is calculated in order to estimate melt rates at the debris/ice interface. The predicted hourly debris surface temperatures and debris internal temperatures provide a good fit to temperatures measured on rock-covered Miage glacier (r2 > 0.94) and the tephra-covered glacier on Villarrica volcano, Chile (r2 > 0.82). The model can also be used to reproduce observed changes in melt rates below debris layers of varying types and thicknesses, an important consideration for the overall mass balance of debris-covered glaciers.