Purpose: In local hyperthermia, precise temperature control throughout the entire target region is key for swift, safe, and effective treatment. In this article, we present a model predictive control (MPC) algorithm providing voxel-level temperature control in magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) and assess the improvement in performance it provides over the current state of the art. Materials and methods: The influence of model detail on the prediction quality and runtime of the controller is evaluated and a tissue mimicking phantom is characterized using the resulting model. Next, potential problems arising from modeling errors are evaluated in silico and in the characterized phantom. Finally, the controller’s performance is compared to the current state-of-the-art hyperthermia controller in side-by-side experiments. Results: Modeling diffusion by heat exchange between four neighboring voxels achieves high predictive performance and results in runtimes suited for real-time control. Erroneous model parameters deteriorate the MPC’s performance. Using models derived from thermometry data acquired during low powered test sonications, however, high control performance is achieved. In a direct comparison with the state-of-the-art hyperthermia controller, the MPC produces smaller tracking errors and tighter temperature distributions, both in a homogeneous target and near a localized heat sink. Conclusion: Using thermal models deduced from low-powered test sonications, the proposed MPC algorithm provides good performance in phantoms. In direct comparison to the current state-of-the-art hyperthermia controller, MPC performs better due to the more finely tuned heating patterns and therefore constitutes an important step toward stable, uniform hyperthermia.