In temperate glacier ice, in situ, besides water veins, there are water lenses, on grain boundaries more or less perpendicular to the direction of maximum pressure p 1 (at the grain scale). Geometry of veins is developed. Grains are modelled as equal tetrakaidecahedra. The stress and temperature fields around a vein at a smaller, microscopic scale are estimated and the water discharge by a Vein is calculated. The time-derivative of the cross-sectional area S of a vein is governed neither by energy dissipation in the water nor by plasticity, but by capillarity effects and salinity. A “vasodilator threshold” p d for water pressure p w in the veins is defined. Normally, P w < P d, then S has a stable value, the same for any orientation of the vein, and the microscopic temperature is uniform. The coefficient of permeability is proportional to (P d-p w)−4, and thus a true Darcy law does not hold. As an application, the percolation of internal meltwater is studied; in an upper boundary layer about 2 m thick this meltwater flows upwards, because in the bulk of the glacier p w is very close to P 1, whereas it is zero at the surface. When, exceptionally, p w > p d, S increases irreversibly. Whether it leads to the formation of “worm-holes” is discussed.