Tasman Glacier, a temperate maritime glacier in the New Zealand Southern Alps, is rapidly receding. Climate warming is resulting in lengthening of the ablation season, meaning crevasses in the accumulation area are becoming exposed at the surface for longer. We combine measurements of air temperature and wind speed from inside crevasses with surface meteorological data, finding that during summer, in-crevasse air temperature is frequently positive, and can at times exceed surface air temperature. Greatest warming occurred in the widest crevasses during clear-sky conditions, but full depth warming of crevasses also occurred at night. Net shortwave radiation contributes to heating of air in the upper regions of crevasses, but turbulent sensible heat transfer was responsible for driving warm air deeper into crevasses. Crevasses orientated to maximise radiation retrieval, and running parallel to wind flow, have the greatest potential for warming and heat storage. We hypothesise a positive feedback loop in the surface energy-balance system, where crevasses entrain and trap heat, which enhances melting, that in turn enlarges the crevasses, enabling greater heat storage and further melting. Energy-balance models that treat accumulation areas of alpine glaciers as homogeneous surfaces will therefore underestimate snow melt and overestimate mass balance.