We combine models for marine ice sheets (which terminate in the ocean) and water flux at the ice–bed interface. The coupled system evolves dynamically due to a positive feedback between ice flow, heat dissipation at the ice stream bed, and basal lubrication. Our results show that, depending on the hydraulic properties of the bed, distinct dynamic regimes can be identified. These regimes include steady streaming, hydraulically controlled oscillations, and thermally controlled oscillations.