The margins of fast-moving ice streams are characterized by steep velocity gradients. Some of these gradients cannot be explained by a temperature-dependent viscosity alone. Laboratory data suggest that water in the ice-grain matrix decreases the ice viscosity; we propose that this causes the strong localization of shear in temperate ice stream margins. However, the magnitude of weakening and its consequences for ice stream dynamics are poorly understood. Here we investigate how the coupling between temperate ice properties, ice mechanics, and drainage of melt water from the ice stream margin alters the dynamics of ice streams. We consider the steady-state ice flow, temperature, water content, and subglacial water drainage in an ice stream cross section. Temperate ice dynamics are modeled as a two-phase flow, with gravity-driven water transport in the pores of a viscously compacting and deforming ice matrix. We find that the dependence of ice viscosity on meltwater content focuses the temperate ice region and steepens the velocity gradients in the ice stream margin. It provides a possible explanation for the steep velocity gradients observed in some ice stream shear margins. This localizes heat dissipation there, which in turn increases the amount of meltwater delivered to the ice stream bed. This process is controlled by the permeability of the temperate ice and the sensitivity of ice viscosity to meltwater content, both of which are poorly constrained properties.