A dynamic cloud masking and filtering algorithm is proposed for the Land Surface Temperature (LST) retrieval from infrared imagery of geostationary satellites. The algorithm uses a modified Kalman Filter (KF) to separate the non-Gaussian error due to clouds from the reference cloud-free LST retrieval error, in order to discriminate and possibly correct for different levels of cloud contamination. This approach was intended to make better use of the important features of the new generation of geostationary satellites, such as the Meteosat Second Generation (MSG) satellites, including their high sampling frequency and the extensive real-time availability of images. The reference surface energy balance model on which the KF is based was simplified to the extent that no information other than top-of-atmosphere solar radiation was required to force the system together with LST measurements. The overall accuracy of the new algorithm, named Cloud Masking with Kalman Filter (CMKF), was tested on the LST retrievals over the Italian peninsula for a 15-day summer period from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor onboard the MSG satellite. As a verification dataset, analogous retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS) were used. The higher spatial resolution of the MODIS LST maps and accompanying cloud masks also allowed us to analyse the results in terms of different levels of fractional cloud cover. The results of these first verification experiments show that the application of the proposed dynamic algorithm improves the LST retrieval, with respect to cloud masking with a classical static algorithm, in two different ways: first, there is a more consistent identification of cloud-free LST data; and second, and more importantly, there is a substantial increase in the quantity of final LST estimates, up to four times more in very cloudy conditions, with the use of prior model predictions at a cost of a very modest increase in the LST root mean squared error (RMSE). Moreover, the higher coefficient of determination in both cases indicates that the algorithm provides LST estimates over a wider range, as it is capable of reconstructing with some accuracy certain lower LST values under cloud cover.