The use of proton resonance frequency shift-based magnetic resonance (MR) thermometry for interventional guidance on abdominal organs is hampered by the constant displacement of the target due to the respiratory cycle and the associated thermometry artifacts. Ideally, a suitable MR thermometry method should for this role achieve a subsecond temporal resolution while maintaining a precision comparable to those achieved on static organs while not introducing significant processing latencies. Here, a computationally effective processing pipeline for two-dimensional image registration coupled with a multibaseline phase correction is proposed in conjunction with high-frame-rate MRI as a possible solution. The proposed MR thermometry method was evaluated for 5 min at a frame rate of 10 images/sec in the liver and the kidney of 11 healthy volunteers and achieved a precision of less than 2 degrees C in 70% of the pixels while delivering temperature and thermal dose maps on the fly. The ability to perform MR thermometry and dosimetry in vivo during a real intervention was demonstrated on a porcine kidney during a high-intensity focused ultrasound heating experiment.