MR thermometry in the liver is challenged by mismatch between baseline and dynamic images caused by motion, leading to temperature errors. To address motion, previous methods had to compromise spatial coverage to increase temporal resolution. We propose a variable-flip-angle (VFA) 3D stack-of-radial technique for combined proton resonance frequency shift (PRF) and T1-based MR thermometry with volumetric coverage and high spatiotemporal resolution. Accurate VFA T1 calculation is achieved by synthesizing B1+ maps that match the liver position in dynamic images. A multi-baseline approach is used for accurate dynamic PRF measurements. Results from non-heating scans demonstrate reliable liver T1 and PRF measurements.