AbstractWe have developed a versatile finite element approach to analyse stresses and displacements induced in thermally thinned and thickened geological structures. Material and geometric non‐linearities form an important aspect of the finite element simulation. The changes in geometry are incorporated by a multipoint constraint procedure. The method takes into account temperature‐dependent variations in rheological properties of the medium, including the presence of a brittle–ductile transition. We illustrate the application of the method for specific geophysical problems associated with the temperature history of the earth's crust at continental margins of the Atlantic