Dynamic and thermodynamic regimes of ice shelves experiencing weak (1 m year−1) to strong (~10 m year−1) basal melting in cold (bottom temperature close to the in situ freezing point) and warm oceans (bottom temperature more than half of a degree warmer than the in situ freezing point) are investigated using a 1-D coupled ice/ocean model complemented with a newly derived analytic expression for the steady state temperature distribution in ice shelves. This expression suggests the existence of a basal thermal boundary layer with thickness inversely proportional to the basal melt rate. Model simulations show that ice shelves afloat in warm ocean waters have significantly colder internal ice temperatures than those that float in cold waters. Our results indicate that in steady states, the mass balance of ice shelves experiencing strong and weak melting is controlled by different processes: in ice shelves with strong melting, it is a balance between ice advection and basal melting, and in ice shelves with weak melting, it is a balance between ice advection and deformation. Sensitivity simulations show that ice shelves in cold and warm oceans respond differently to increase of the ocean heat content. Ice shelves in cold waters are more sensitive to warming of the ocean bottom waters, while ice shelves in warm waters are more sensitive to shallowing of the depth of the thermocline.