The spatio-temporal distribution of air temperature over mountain glaciers can demonstrate complex patterns, yet it is often represented simplistically using linear vertical temperature gradients (VTGs) extrapolated from off-glacier locations. We analyse a network of centreline and lateral air temperature observations at Tsanteleina Glacier, Italy, during summer 2015. On average, VTGs are steep (<−0.0065 °C m−1), but they are shallow under warm ambient conditions when the correlation between air temperature and elevation becomes weaker. Published along-flowline temperature distribution methods explain centreline observations well, including warming on the lower glacier tongue, but cannot estimate lateral temperature variability. Application of temperature distribution methods improves simulation of melt rates (RMSE) in an energy-balance model by up to 36% compared to the environmental lapse rate extrapolated from an off-glacier station. However, results suggest that model parameters are not easily transferable to glaciers with a small fetch without recalibration. Such methods have potential to improve estimates of temperature across a glacier, but their parameter transferability should be further linked to the glacier and atmospheric characteristics. Furthermore, ‘cold spots’, which can be >2°C cooler than expected for their elevation, whose occurrence is not predicted by the temperature distribution models, are identified at one-quarter of the measurement sites.