Meltwater is important to understanding glacier health and dynamics. Since melt measurements are uncommon, ice ablation estimates are often based on models including the positive degree day (PDD) model. The PDD estimate is popular since it only requires air temperature as input, but suffers from the lack of physical motivation of an energy-balance model. We present a physics-based alternative to the PDD model that still only takes air/surface temperature as input. The model resembles the PDD model except accounting for time lags in ablation when cold ice needs to be warmed. The model is expressed as a differential equation with a single extra parameter related to the efficiency of heating a near-surface layer of ice. With zero thickness, the model reduces to the PDD model, providing a physical basis for the PDD model. Applying the model to data from Greenland, it improves modestly upon the PDD model, with the main improvement being better prediction of early season melting. This new model is a useful compromise, with some of the physics of more realistic models and the simplicity of a PDD model. The model should improve estimates of meltwater production and help constrain PDD parameters when empirical calibration is challenging.