Hydrocarbon generation is a temperature-dependent process and the prediction of hydrocarbon generation in basin modelling requires the crustal heat flow history to be predicted. Tectonically, the Faroe–Shetland Basin (FSB) has been subjected to a number of Cretaceous rifting events, followed in the Tertiary by Balder volcanism and, finally, by Oligo-Miocene inversion. In this study the thermal history of the FSB is derived using two independent methods (rifting–volcanic–subsidence history and maturation). The methodology is described using two wells (204/19-1 and 205/22-1) in the southern FSB. The vitrinite reflectance results predicted by the PresRo® model, which was devised for modelling maturation in overpressured basins such as the FSB, produced predicted vitrinite reflectances that matched the measured values. The method was then applied to a pseudowell within the Foinaven sub-basin, and the predicted vitrinite reflectance values for the Kimmeridge Clay Formation source at 8 km depth indicate that the source is still mature for oil generation due to the extensive retardation induced by the highly overpressured, argillaceous Mesozoic sediments.