Land surface temperature (LST) serves as a fundamental metric for assessing land-atmosphere interactions and is increasingly recognized for its importance in diverse disciplines such as climatology, public health, and energy resource management. This research investigates the variability of LST in the Patna district, utilizing data from the Land satellite (LANDSAT), also recognized as the Earth Resources Technology Satellite (ERTS), alongside the Google Earth Engine (GEE), which employs machine learning algorithms for analysis. Moreover, the study aims to ascertain the LST specific to the Patna district and to elucidate the relationship and correlation between LST and the Normalized Difference Built-up Index (NDBI) to enhance land-use planning and environmental management within the urban context. The NDBI is derived through the application of machine learning techniques and satellite-derived data. The GEE platform facilitates streamlined access to all satellite datasets and incorporates a JavaScript-based algorithm for the examination of LST correlations with the built-up areas. The current investigation has been conducted utilizing Landsat datasets covering a three-month period during the summer quartile, specifically in April, May, and June for the years 2005, 2010, 2015, 2020, 2022, and 2023. The findings indicate that LST exhibits a positive correlation with NDBI.