Accurately modeling the deformation of temperate glacier ice, which is at its pressure-melting temperature and contains liquid water at grain boundaries, is essential for predicting ice sheet discharge to the ocean and associated sea-level rise. Central to such modeling is Glen’s flow law, in which strain rate depends on stress raised to a power of n = 3 to 4. In sharp contrast to this nonlinearity, we found by conducting large-scale, shear-deformation experiments that temperate ice is linear-viscous ( n ≈ 1.0) over common ranges of liquid water content and stress expected near glacier beds and in ice-stream margins. This linearity is likely caused by diffusive pressure melting and refreezing at grain boundaries and could help to stabilize modeled responses of ice sheets to shrinkage-induced stress increases.