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Switched-actuator systems with setup times (SAcSSs) are systems in which the actuator configuration has to be switched during operation, and where the switching induces non-negligible actuator downtime. Optimally controlling SAcSSs requires the online solving of both a discrete actuator allocation problem, in which the switch-induced actuator downtime is taken into account, as well as an optimization problem for the (typically continuous) control inputs. Mixed-integer model predictive control (MI-MPC) offers a powerful framework for tackling such problems. However, the efficient modeling of SAcSSs for MI-MPC is not straightforward, and real-time feasibility is often a major hurdle in practice. It is the objective of this paper to provide an intuitive and systematic modeling procedure tailored to SAcSSs, which is specifically designed to allow for user-friendly controller synthesis, and to yield efficient MI-MPCs. We apply these new results in a case study of large-volume magnetic-resonance-guided high-intensity focused ultrasound hyperthermia, which involves the heating of tumors (using real-valued local heating controls, as well as discrete range-extending actuator relocation during which no heating is allowed) to enhance the efficacy of radio- and chemotherapy.