Coupled MR Elastography (MRE) and Proton Resonance Frequency Shift (PRFS) thermometry have been proposed for the monitoring of thermal ablations. Fat-referenced PRFS thermometry based on water-fat separation allows correcting for errors caused by field drift. We propose a new approach for combined MRE and fat-referenced PRFS thermometry, allowing for improved thermometry while keeping the acquisition time unchanged. This is obtained by varying simultaneously TE and MRE phase offsets for water-fat separation and MRE, respectively. Feasibility of the method was demonstrated in a water/fat phantom during a High Intensity Focused Ultrasound ablation experiment, in which elasticity and temperature changes were monitored.