Similar to the coldest terrestrial periglacial regions like Yakutia (Siberia), the planet Mars exhibits wide outflow channels. This analogy and the presence of permanent ground ice suggest that thermal erosion have existed during Martial fluvial outbursts 3000 m.y. ago. Thermal erosion here is considered to be the result of ground thawing produced by heat transfer between the water flow and the frozen ground, followed by a transport of unfrozen sediments. This paper proposes a qualitative explanation of thermal erosion with the help of some physical models. From the quantitative point of view, two thermal mathematical models are proposed and discussed. The zones undergoing the most efficient erosion are river banks. The first model studied here describes extreme thermomechanical actions: A constant thermal flux on the ground surface produces ground thaw, and the unfrozen sediments are immediately removed by water flow. It is an ablation model. It allows a theoretical evaluation of the river bank recession. Validity of theoretical estimations is acquired by comparing the calculations to the observed backwearing of the banks of some Siberian rivers which can reach 25 m yr-1. Thermal erosion acting upon the bottom of wide rivers (on Mars or in Siberia as well) is a very complex mechanism. Indeed, the mathematical modeling requires the study of interaction between thermal processes and transport of sediments laws. These laws are not yet well defined and are very difficult to establish. Thus another model presented in this paper concerns only one-dimensional thermal actions of water flow upon the bottom of wide rivers. It considers fluvial flow at positive Celsius temperature producing a thermal flux from the bottom to the initially frozen semi-infinite ground. This model considers a constant convective heat transfer coefficient and allows an estimation of the thickness of the thawed ground beneath the river (talik). Calculated thickness of the melted ground is give in the paper for different periods of time. ¿ American Geophysical Union 1994