To find the temperature rise for high power density yokeless and segmented armature (YASA) axial flux permanent magnet synchronous (AFPMSM) machines quickly and accurately, a 3D lumped parameter thermal model is developed and validated experimentally and by finite element (FE) simulations on a 4 kW YASA machine. Additionally, to get insight in the thermal transient response of the machine, the model accounts for the thermal capacitance of different machine components. The model considers the stator, bearing, and windage losses, as well as eddy current losses in the magnets on the rotors. The new contribution of this work is that the thermal model takes cooling via air channels between the magnets on the rotor discs into account. The model is parametrized with respect to the permanent magnet (PM) angle ratio, the PM thickness ratio, the air gap length, and the rotor speed. The effect of the channels is incorporated via convection equations based on many computational fluid dynamics (CFD) computations. The model accuracy is validated at different values of parameters by FE simulations in both transient and steady state. The model takes less than 1 s to solve for the temperature distribution.