Land surface temperatures (LSTs) can be approximated from brightness temperatures observed from satellites. Estimation errors between observed brightness temperatures and a brightness temperature model of a given pixel would provide information for a pixel concerned. Robust fitting of observed Diurnal Temperature Cycle (DTC) taken over a day of a given pixel without cloud cover and other abnormally conditions such as fire can give a data based brightness temperature model for a given pixel. In this paper, diurnal brightness temperatures received from the METEOSAT Second Generation (MSG) satellite were interpolated for missing data based on a model, and a performance test was performed by comparing a new approach based on robust modelling with previous algorithms implemented on MSG data: An algorithm based on pseudo-physical modelling of the DTC and an algorithm based on Reproducing Kernel Hilbert Space (RKHS) interpolator. The simulation results show that the new approach outperforms the previous used criteria, in the sense that the true nonlinear model is more often found.