Monitoring Land Surface Temperature (LST) from satellite remote sensing requires an accurate correction of the atmospheric effects. Although thermal remote sensing techniques have advanced significantly over the past few decades, to date, single-band pixel-by-pixel atmospheric correction of full thermal images is unsolved. In this work, we introduce a new Single-Band Atmospheric Correction (SBAC) tool that provides pixel-by-pixel atmospheric correction parameters regardless of the pixel size. The SBAC tool uses National Centers of Environmental Prediction (NCEP) profiles as inputs and, as a novelty, it also accounts for pixel elevation through a Digital Elevation Model (DEM). Application of SBAC to 19 Landsat 7-ETM+ scenes shows the potential of the proposed pixel-by-pixel atmospheric correction to capture terrain orography or atmospheric variability within the scene. LST estimation yields negligible bias and an RMSE of ±1.6 K for the full dataset. The Landsat Atmospheric Correction Tool (ACT) is also considered for comparison. SBAC-ACT LST deviations are analyzed in terms of distance to the image center, surface elevation, and spatial distribution of the atmospheric water content. Differences within 3 K are observed. These results give us the first insight of the potential of SBAC for the operational pixel-by-pixel atmospheric correction of full thermal images. The SBAC tool is expected to help users of satellite single-channel thermal sensors to improve their LST estimates due to its simplicity and robustness.