Climatic warming is shown to be capable of inducing shear heating instability and basal melting in a model ice sheet that is creeping slowly downslope. Growth times of the instability are calculated from a nonlinear analysis of temperature and flow in the model ice sheet whose surface undergoes a prescribed increase of temperature. The source of instability lies in the decrease of maximum ice thickness for steady downslope creep with increasing surface temperature. A surface temperature increase of 5 to 10 K can cause instability on a 104 year time scale for realistic ice rheology. The instability occurs suddenly after a prolonged period of dormancy. The instability might be relevant to the East Antarctic ice sheet. Warming associated with the Holocene interglacial epoch that heralded the end of the last ice age may have set the East Antarctic ice sheet on a course toward widespread instability some 104 years later. The present CO2‐induced climate warming is also a potential trigger for instability and basal melting of the East Antarctic ice sheet.