Axial-Flux Permanent Magnet (AFPM) machines have gained popularity over the past few years due to their compact design. Their application can be found, for example, in the automotive and medical sectors. For typically considered materials, excessive heat can be generated, causing possible irreversible damage to the magnets, bonding, or other structural parts. In order to optimize cooling, knowledge of the flow and the consequent temperature distribution is required. This paper discusses the flow types and heat transfer present inside a typical AFPM machine. An Isogeometric Analysis (IGA) laminar-energy model is developed using the Nutils open-source Python package. The developed analysis tool is used to study the effects of various important design parameters, such as the air-inlet, the gap-length, and the rotation speed on the heat transfer in an AFPM machine. It is observed that the convective heat transfer at the stator core is negatively affected by adding an air-inlet. However, the heat dissipation of the entire stator improves as convective heat transfer occurs within the air-inlet.