Failure conditions in soils at elevated temperatures appear to be strongly dependent on the history of the application of stress and temperature. Four cases of such history leading to various modes of failure are identified and interpreted in terms of Thermal Cam-Clay models. Particular attention is given to the influence of thermal variability on the coefficient of the critical state, M, or the angle of internal friction. A detailed analysis of the material history offers an explanation of an apparent confusion about whether the soil strength is decreased or increased by temperature. In a companion paper (Hueckel et al., 2009), numerical analysis of the development of axisymmetric thermal and stress fields around a cylindrical heat source suggests that thermal failure may arise in conditions that are not connected to any mechanically critical situation.