In magnetic resonance (MR) thermometry, first and second magnetic resonance data that are acquired sequentially, from which a phase shift is determined between a measurement phase and a reference phase. In a first region of an examined person, the measurement phase is determined from the second magnetic resonance data and the reference phase is determined from the first magnetic resonance data. In a second region of the examined person, both the reference phase and measurement phase are determined from the second magnetic resonance data. Techniques for reference-based magnetic resonance thermometry and reference-free magnetic resonance thermometry can be applied.