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 end-point. However, the precision of real time MR-thermometry is generally limited by the available signal to noise ratio (SNR). In order to improve the efficiency of applications, which are based on online temperature measurements, temporal filtering can be employed. Here, we propose a novel digital filter combining extended Kalman filtering with a temperature predictive model based on the bio heat transfer equation. The proposed approach is evaluated on simulated datasets and on MR-guided HIFU ablation experiments on ex-vivo porcine muscle. The proposed filter showed a significantly improved precision and accuracy in comparison to an optimized FIR filter.