Near-surface air temperature (Ta) is highly important for modelling glacier ablation, though its spatiotemporal variability over melting glaciers still remains largely unknown. We present a new dataset of distributed Ta for three glaciers of different size in the south-east Tibetan Plateau during two monsoon-dominated summer seasons. We compare on-glacier Ta to ambient Ta extrapolated from several local off-glacier stations. We parameterise the along-flowline sensitivity of Ta on these glaciers to changes in off-glacier temperatures (referred to as "temperature sensitivity") and present the results in the context of available distributed on-glacier datasets around the world. Temperature sensitivity decreases rapidly up to 2000 3000 m along the down-glacier flowline distance. Beyond this distance, both the Ta on the Tibetan glaciers and global glacier datasets show little additional cooling relative to the off-glacier temperature. In general, Ta on small glaciers (with flowline distances < 1000 m) is highly sensitive to temperature changes outside the glacier boundary layer. The climatology of a given region can influence the general magnitude of this temperature sensitivity, though no strong relationships are found between along-flowline temperature sensitivity and mean summer temperatures or precipitation. The terminus of some glaciers is affected by other warm-air processes that increase temperature sensitivity (such as divergent boundary layer flow, warm up-valley winds or debris/valley heating effects) which are evident only beyond ∼ 70 % of the total glacier flowline distance. Our results therefore suggest a strong role of local effects in modulating temperature sensitivity close to the glacier terminus, although further work is still required to explain the variability of these effects for different glaciers. © 2021 Author(s).