A finite-difference numerical model is used to simulate the temperature profile at the center of an ice sheet throughout the course of a glaciation. The ice sheet is gradually built to a thickness of 3000 m over about 10 000 years, starting on permafrost. A geothermal heat flux is applied at large depth. For an initial surface temperature of –12.5°C, our model shows that basal melting occurs 72000 years after the onset of the glaciation. The important parameters determining the basal temperatures are the initial temperature of the ice and substrate, the rate of downward advection of cold ice and, to a lesser extent, the thickness of the ice sheet. The growth history of the ice sheet does not significantly influence the time at which basal melting occurs. Our results show the possibility that the central parts of the continental ice sheets were cold-based for a significant part of their existence. Heating due to the geothermal heat flux cannot account for basal melting during most or all of a glacial cycle. These results may help to explain the existence of preserved land forms under the ice sheets.