Magnetic resonance information acquired by a movable magnetic resonance instrument is used to monitor hyperthermia treatments such as tissue ablation. The instrument may include both the magnetic resonance equipment and an energy applicator such as a high intensity focused ultrasound unit. The treatment can be conducted under automatic control after the operator marks a treatment volume on an image of the subject, such as a magnetic resonance image acquired using the movable magnetic resonance instrument. The automatic treatment can be based on interpolation of tissue response curves at plural test points near the treatment volume. The system can also provide automatic supervisory control during manual operation, to prevent application of heat to sensitive anatomical structures.