A dynamical model governing the variations of ice-sheet volume, basal-water amount and ice-surge flux has been formulated in its simplest form, based on fundamental thermomechanical properties of ice sheets governing the basal-melting process. This model includes the effects of the geothermal flux, internal thermal advection and basal friction, the latter two factors being particularly important in regulating the bottom temperature and bringing it to the melting point, i.e. to a state vulnerable to catastrophic ice surges. It is shown that, for certain values of the unknown rate constants, such a model can exhibit oscillations on roughly the same scale as observed Heinrich events, even when external climatic changes are neglected, which would support the view that such events are an internal properly of ice sheets.