A medical apparatus (300, 400, 500, 600, 700) comprises a heating system (304) for heating a target zone (324) of a subject (320), wherein the energy density in a predefined volume is modeled (338) using a thermal model and a processor (330) for controlling (340) the heating system (304). The medical apparatus (300, 400, 500, 600, 700) further comprises a memory (336) containing machine executable instructions, wherein execution of the instructions causes the processor (330) to receive (100, 200, 342) a treatment plan, wherein execution of the instructions further causes the processor (330) to repeatedly: heat (102, 202, 344) the target zone (324) during alternating heating periods and cooling periods by controlling (340) the heating system (304) using the treatment plan and calculate (104, 204, 346) a present energy density map (350) in a predefined volume using the treatment plan and the thermal model, wherein the present energy density is repeatedly updated (348) during the heating of the target zone (324).