The frequency of heatwave events has increased in recent decades because of global warming. Satellite observed Land Surface Temperature (LST) is a widely used parameter for assessing heatwaves. It provides a wide spatial coverage compared to surface air temperature measured at weather stations. However, LST quality is limited by cloud contamination. Because heatwaves have a limited temporal frame, having a full and cloud-free complement of LST for that period is necessary. In this letter, we explore gap-filling of LST using spatial features like land cover, elevation and vegetation indices in a machine learning approach. We use a seamless open and free daily vegetation index product which is paramount to the success of our study. We create a Random Forest model that provides a ranking of features relevant for predicting LST. We compare the output of our model to an established spatiotemporal gap-filling algorithm to validate the predictive capability of our model. This study validates machine learning as a suitable tool for filling gaps in satellite LST. In addition, we acknowledge that while time is an important factor in predicting LST, additional information on vegetation can improve the predictions of a model This dataset covers gap-filled MODIS LST using machine learning for three heatwave periods in Estonia. The RMSE of the model on the test data is 1.37. Jupyter notebooks used in this project can be found at https://github.com/kwazineutin/Gapfilling-Satellite-LST-with-ML