A finite element model was developed to predict the spatial and temporal variation of heat generation and temperature in FSSW of aluminium and magnesium alloys. Heating by friction and bulk plasticity is computed at intervals using small-strain elastic-plastic analysis for a small fraction of one tool rotation. This runs in parallel with a conventional thermal analysis running for the whole weld cycle. The model was tested at two tool rotation speeds with experimental data for three wrought aluminium alloys, and two casting alloys (one aluminium and one magnesium). Heat generation history was found to be remarkably similar for both rotation speeds and across all five alloys. A key aspect of the model is the use of a physically-based kinematic boundary condition at the tool-workpiece interface, with the surface velocity profile having an inner sticking region and an outer slipping region. The method shows the potential for rapid calculation of heat input and temperature fields in large strain frictional processes such as FSSW, without recourse to fully coupled explicit FE analysis.