A high spatio-temporal resolution land surface temperature (LST) is necessary for various research fields because LST plays a crucial role in the energy exchange between the atmosphere and the ground surface. The moderate-resolution imaging spectroradiometer (MODIS) LST has been widely used, but it is not available under cloudy conditions. This study proposed a novel approach for reconstructing all-sky 1 km MODIS LST in South Korea during the summer seasons using various data sources, considering the cloud effects on LST. In South Korea, a Local Data Assimilation and Prediction System (LDAPS) with a relatively high spatial resolution of 1.5 km has been operated since 2013. The LDAPS model’s analysis data, binary MODIS cloud cover, and auxiliary data were used as input variables, while MODIS LST and cloudy-sky in situ LST were used together as target variables based on the light gradient boosting machine (LightGBM) approach. As a result of spatial five-fold cross-validation using MODIS LST, the proposed model had a coefficient of determination (R2) of 0.89–0.91 with a root mean square error (RMSE) of 1.11–1.39 °C during the daytime, and an R2 of 0.96–0.97 with an RMSE of 0.59–0.60 °C at nighttime. In addition, the reconstructed LST under the cloud was evaluated using leave-one-station-out cross-validation (LOSOCV) using 22 weather stations. From the LOSOCV results under cloudy conditions, the proposed LightGBM model had an R2 of 0.55–0.63 with an RMSE of 2.41–3.00 °C during the daytime, and an R2 of 0.70–0.74 with an RMSE of 1.31–1.36 °C at nighttime. These results indicated that the reconstructed LST has higher accuracy than the LDAPS model. This study also demonstrated that cloud cover information improved the cloudy-sky LST estimation accuracy by adequately reflecting the heterogeneity of the relationship between LST and input variables under clear and cloudy skies. The reconstructed all-sky LST can be used in a variety of research applications including weather monitoring and forecasting.