In this paper, the effect of some geometrical parameters on the steady state average temperature of the stator core, the winding and the permanent magnets of the yokeless and segmented armature (YASA) axial flux permanent magnet synchronous machine (AFPMSM) is studied. The geometrical parameters selected for the study are the air gap length, the inward heat extraction fin thickness and the permanent magnet thickness. These parametric studies make it possible to obtain a better trade-off between power density and efficiency. These investigations are very helpful in correlating the values of the geometrical parameters to some specific desired performance criteria like not going below some desired minimum efficiency, limiting the temperature of specific part to some maximum value for maximization of lifetime and also determination of the allowed speed range to limit the temperatures lower than the critical values. This is important specifically for the synchronous machines due to the fact that the speed value affects both the losses and the heat transfer convection coefficients. The air gap length has a direct effect on the overall machine losses and the air gap convection coefficient and hence on the temperature of the machine. As the fins are between the stator windings, a thicker fin reduces the space for copper windings and hence increases the losses, but at the same time improves heat evacuation. In addition, the effect on the temperature is studied of the speed variation, which influences both the losses and the convection coefficients of the machine. Every study is made based on coupled electromagnetic and thermal models. The results are obtained from analytical electromagnetic and thermal models verified by finite element simulations and validated experimentally on a 4 kW yokeless and segmented armature axial flux machine.