The invention provides for a medical apparatus (400, 500, 600, 700, 800) comprising a magnetic resonance imaging system (402) for acquiring magnetic resonance thermometry data (442) from a subject (418). The magnetic resonance imaging system comprises a magnet (404) with an imaging zone (408). The medical apparatus further comprises a memory (432) for storing machine executable instructions (460, 462, 464, 466, 10, 660). The medical apparatus further comprises a processor (426) for controlling the medical apparatus, wherein execution of the machine executable instructions causes the processor to: acquire (100, 200, 300) the magnetic resonance thermometry data from multiple slices (421, 421′, 421″) within the imaging zone by controlling the magnetic resonance imaging system; and interpolate (102, 202, 204, 302, 304) a three dimensional thermal dose estimate (444) in accordance with the magnetic resonance thermometry data.