This paper investigates the thermodynamic consequences of introducing basal sliding into a two-dimensional ice sheet model. The coupling of ice sheet form, flow field, and temperature evolution gives rise to limit cycles in the basal thermal regime of the ice sheet. Typical periods are 4000 to 5000 years and up to 45% of the ice sheet length can be affected. The limit cycles are caused by the switching on and off of sliding as basal ice reaches the pressure melting point. An analysis of the various heat fluxes at the ice sheet base stresses the roles of vertical diffusion and the heat generated by internal deformation and sliding in controlling the period and extent of the cycles. Limit cycles are found to persist in the face of various climatic (snow accumulation rate and air temperature) parameterizations, as well as for different basal sliding parameterizations. The types of oscillation change produced by varying accumulation rate is particularly interesting. Several distinct patterns of behavior are observed. For low accumulation rate ice sheets, a period of 6000--7000 years is dominant; for medium accumulation rate ice sheets, the 3000 to 4000 year period is dominant; while for larger accumulation rates, the oscillations become highly irregular with long (>10,000 years) periods. ¿ American Geophysical Union 1995