A medical apparatus (300, 400, 500, 600) includes a magnetic resonance imaging system (301). The medical apparatus further includes a memory (330) containing instructions (350, 352, 354, 456, 458, 460) for execution by a processor (324). Execution of the instructions causes the processor to acquire (102, 202) baseline magnetic resonance data (332) and reconstruct (104, 204) a first image (334) using the baseline magnetic resonance data. Execution of the instructions further causes the processor acquire (106, 212) undersampled magnetic resonance data (336), which is undersampled in k- space in comparison to the baseline magnetic resonance data. Execution of the instructions further causes the processor reconstruct (108, 214) a second image (338) using the undersampled magnetic resonance data and the first image. The second image is reconstructed using an image ratio constrained reconstruction algorithm (354). A temperature map (340) is calculated (110, 216) using the second image.