Proton resonance frequency shift (PRFS) MR thermometry (MRT) is the generally preferred method for monitoring thermal ablation, typically implemented with gradient-echo (GRE) sequences. Standard PRFS MRT is based on the subtraction of a temporal reference phase map and is, therefore, intrinsically sensitive to tissue motion (including deformation) and to external perturbation of the magnetic field. Reference-free (or reference-less) PRFS MRT has been previously described by Rieke and was based on a 2-D polynomial fit performed on phase data from outside the heated region, to estimate the background phase inside the region of interest. While their approach was undeniably a fundamental progress in terms of robustness against tissue motion and magnetic perturbations, the underlying mathematical formalism requires a thick unheated border and may be subject to numerical instabilities with high order polynomials. A novel method of reference-free PRFS MRT is described here, using a physically consistent formalism, which exploits mathematical properties of the magnetic field in a homogeneous or near-homogeneous medium. The present implementation requires as input the MR GRE phase values along a thin, nearly-closed and unheated border. This is a 2-D restriction of a classic Dirichlet problem, working on a slice per slice basis. The method has been validated experimentally by comparison with the “ground truth” data, considered to be the standard PRFS method for static ex vivo tissue. “Zero measurement” of the gradient-echo phase baseline was performed in healthy volunteer liver with rapid acquisition (300 ms/image). In vivo data acquired in sheep liver during MR-guided high intensity focused ultrasound (MRgHIFU) sonication were post-processed as proof of applicability in a therapeutic scenario. Bland and Altman mean absolute difference between the novel method and the “ground truth” thermometry in ex vivo static tissue ranged between 0.069 °C and 0.968 °C, compared to the inherent “white” noise SD of 0.23 °C. The accuracy and precision of the novel method in volunteer liver were found to be on average 0.13 °C and respectively 0.65 °C while the inherent “white” noise SD was on average 0.51 °C. The method was successfully applied to large ROIs, up to 6.2 cm inner diameter, and the computing time per slice was systematically less than 100 ms using C++. The current limitations of reference-free PRFS thermometry originate mainly from the need to provide a nearly-closed border, where the MR phase is artifact-free and the tissue is unheated, plus the potential need to reposition that border during breathing to track the motion of the anatomic zone being monitored.A reference-free PRFS thermometry method based on the theoretical framework of harmonic functions is described and evaluated here. The computing time is compatible with online monitoring during local thermotherapy. The current reference-free MRT approach expands the workflow flexibility, eliminates the need for respiratory triggers, enables higher temporal resolution, and is insensitive to unique-event motion of tissue.