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Land Surface Temperature (LST) is an important resource for a variety of tasks. The data are mostly free of charge and combine high spatial and temporal resolution with reliable data collection over a historical timeframe. When remote sensing is used to provide LST data, such as the MODA11 product using information from the MODIS sensors attached to NASA satellites, data acquisition can be hindered by clouds or cloud shadows, occluding the sensors' view on different areas of the world. This makes it difficult to take full advantage of the high resolution of the data. A common solution to interpolating LST data is statistical interpolation methods, such as fitting polynomials or thin plate spine interpolation. These methods have difficulties in incorporating additional knowledge about the research area and learning local dependencies that can help with the interpolation process. We propose a novel approach to interpolating remote sensing LST data in a fixed research area considering local ground-site air temperature measurements. The two-step approach consists of learning the LST from air temperature measurements, where the ground-site weather stations are located, and interpolating the remaining missing values with partial convolutions within a U-Net deep learning architecture. Our approach improves the interpolation of LST for our research area by 44% in terms of RMSE, when compared to state-of-the-art statistical methods. Due to the use of air temperature, we can provide coverage of 100%, even when no valid LST measurements were available. The resulting gapless coverage of high resolution LST data will help unlock the full potential of remote sensing LST data. [ABSTRACT FROM AUTHOR]