In order to account for the effects of debris cover in model scenarios of the response of glaciers to climate change and water resource planning, it is important to know the distribution and thickness of supraglacial debris and to monitor its change over time. Previous attempts to map surface debris thickness using thermal band remote sensing have relied upon time-specific empirical relationships between surface temperature and thickness, limiting their general applicability. In this paper, we develop a physically based model that utilizes Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) thermal band remotely sensed imagery and is based on a solution of the energy balance at the debris surface. The model is used to estimate debris thickness on Miage glacier, Italy, and is validated using field debris-thickness measurements and a previously published debris-thickness map. The temporal transferability of the model is demonstrated through successful application to a separate ASTER image from a different year using reanalysis meteorological input data. This model has the potential to be used for regional-scale supraglacial debris-thickness mapping and monitoring for debris up to at least 0.50 m thickness, but improved understanding of the spatial patterns of air temperature, aerodynamic roughness length and thermal properties across debriscovered glaciers is needed.