Abstract-Real time magnetic resonance (MR) thermometry is gaining clinical importance for monitoring and guiding high intensity focused ultrasound (HIFU) ablations of tumorous tissue. The temperature information can be employed to adjust the position and the power of the HIFU system in real time and to determine the therapy endpoint.The requirement to resove both physiological motion on mobile organs and the rapid temperature variations induced by state-ofthe art high-power HIFU systems requires fast MRI-acquisition schemes, which are generally hampered by low signal to noise ratios (SNR). This directly limits the precision of real time MR-thermometry and thus in many cases the feasability of sophisticated control algorithms. To overcome these limitations, temporal filtering of the temperature has been suggested in the past, which has generally an adverse impact on the accuracy and latency of the filtered data.Here, we propose a novel model based digital filter combining an extended Kalman filter (EKF) with a predictive model of the temperature based on the bio heat transfer equation. This filter aims to improve the precision of MR-thermometry while monitoring and adapting its impact on the accuracy using the formalism of adaptive extended Kalman filtering. An additional outlier rejection addresses the problem of sparse artifacted temperature points. The filter was evaluated and compared to a matched FIR filter using simulated data, HIFU experiments on phantoms and in vivo data obtained during HIFU ablations on porcine kidneys. The filter provides improved artefact and noise reduction, while having a minimal impact on accuracy and latency.