Wide outflow channels occur both in Siberia and on the planet Mars. In Siberia, thermal erosion results from ground thawing produced by the heat transfer from the flow of water to the frozen ground. We suggest that relatively warm floods on Mars could enlarge outflow channels by a combination of thermal and mechanical erosion along frozen river banks. A one-dimensional model is proposed to estimate the thermal erosion efficiency. A first test of this model is a comparison of results with experiments carried out in a cold chamber. A hydraulic channel allows measurements of the thawing line propagation, as well as the thermal erosion rate, in simulated ground ice that is subjected to warm water flow. Various laboratory simulations demonstrate the validity of the mathematical model for the range of laboratory conditions. This model is then applied to a range of possible current and ancient Martian conditions. ¿ 1999 American Geophysical Union