Magnetocaloric cooling is an emerging technology for room temperature refrigeration which has the potential to surpass the established gas-vapor compression refrigeration system in terms of efficiency while eliminating direct greenhouse gas emissions. It is based on the magnetocaloric effect, i.e., the temperature change exhibited by certain ferromagnetic materials upon magnetization and demagnetization. Key components of application-aimed systems are the Active Magnetic Regenerator (AMR) and the permanent magnet assembly. The system operates with a periodically changing fluid flow alongside the cyclic magnetization and demagnetization of the AMR, achieved by the movement of the permanent magnet assembly. This results in a heightened temperature span along the AMR and an output of cooling power. Numerical optimization of the system is key to achieving high performance and energy efficiency. Recently, Wiesheu et al. demonstrated that topology and shape optimization based on field profiles can significantly improve the design. However, simulation and optimization of AMR and assembly are still performed sequentially. The AMR is studied using a given magnetization profile, while the magnet assembly is arranged to maximize the generated air gap field. This work proposes the coupling of magnet and AMR simulation: the generated magnetic field is computed and given as input to a transient convection-diffusion problem describing the heat transfer in the AMR. When the cyclic steady state is found, key performance metrics, such as cooling power or coefficient of performance, are calculated. This is suitable for use in the objective function of an optimization. In this way, the permanent magnet assembly can be optimized for system performance rather than a surrogate metric.