This paper investigates the thermal behavior of axial flux synchronous permanent-magnet machines (AFSPMMs) through a 3-D thermal-magnetic finite-element analysis (FEA). This paper offers a systematic approach to magnetothermal FEA. The considered axial flux machine is wound on a soft magnetic compound core. The computation of thermal field is performed via a coupled thermal and fluid-dynamical model based on FEA, where the thermal sources are obtained from a DC current flow model and a magnetostatic model. This paper includes an overview of the finite-element method (FEM) model implementation. Simulation results are presented, and, to validate the model, the simulated surface temperature rise of the motor parts is compared by experimental data.