Near-surface air temperature is an important determinant of the surface energy balance of glaciers and is often represented by a constant linear temperature gradients (TGs) in models. Spatio-temporal variability in 2 m air temperature was measured across the debris-covered Miage Glacier, Italy, over an 89 d period during the 2014 ablation season using a network of 19 stations. Air temperature was found to be strongly dependent upon elevation for most stations, even under varying meteorological conditions and at different times of day, and its spatial variability was well explained by a locally derived mean linear TG (MG–TG) of −0.0088°C m−1. However, local temperature depressions occurred over areas of very thin or patchy debris cover. The MG–TG, together with other air TGs, extrapolated from both on- and off-glacier sites, were applied in a distributed energy-balance model. Compared with piecewise air temperature extrapolation from all on-glacier stations, modelled ablation, using the MG–TG, increased by <1%, increasing to >4% using the environmental ‘lapse rate’. Ice melt under thick debris was relatively insensitive to air temperature, while the effects of different temperature extrapolation methods were strongest at high elevation sites of thin and patchy debris cover.