Abstract. The high temporal resolution of data acquisition by geostationary satellites and their capability to resolve the diurnal cycle allows for the retrieval of a valuable source of information about geophysical parameters. In this paper, we implement a Kalman filter approach to apply temporal constraints on the retrieval of surface emissivity and temperature from radiance measurements made from geostationary platforms. Although we consider a case study in which we apply a strictly temporal constraint alone, the methodology will be presented in its general four-dimensional, i.e., space-time, setting. The case study we consider is the retrieval of emissivity and surface temperature from SEVIRI (Spinning Enhanced Visible and Infrared Imager) observations over a target area encompassing the Iberian Peninsula and northwestern Africa. The retrievals are then compared with in situ data and other similar satellite products. Our findings show that the Kalman filter strategy can simultaneously retrieve surface emissivity and temperature with an accuracy of ± 0.005 and ± 0.2 K, respectively.