Near-surface air temperature, typically measured at a height of 2 m, is the most important control on the energy exchange and the melt rate at a snow or ice surface. It is distributed in a simplistic manner in most glacier melt models by using constant linear lapse rates, which poorly represent the actual spatial and temporal variability of air temperature. In this paper, we test a simple thermodynamic model proposed by Greuell and Böhm in 1998 as an alternative, using a new dataset of air temperature measurements from along the flowline of Haut Glacier d'Arolla, Switzerland. The unmodified model performs little better than assuming a constant linear lapse rate. When modified to allow the ratio of the boundary layer height to the bulk heat transfer coefficient to vary along the flowline, the model matches measured air temperatures better, and a further reduction of the root-mean-square error is obtained, although there is still considerable scope for improvement. The modified model is shown to perform best under conditions favourable to the development of katabatic winds – few clouds, positive ambient air temperature, limited influence of synoptic or valley winds and a long fetch – but its performance is poor under cloudy conditions.