Nowadays, most of the datasets leveraging space-borne Earth Observation (EO) data are based on high-end levels products, which are ortho-rectified, coregistered, calibrated, and further processed to mitigate the impact of noise and distortions. Nevertheless, given the growing interest to apply Artificial Intelligence (AI) onboard satellites for time-critical applications, such as natural disaster response, providing raw satellite images could be useful to foster the research on energy-efficient pre-processing algorithms and AI models for onboard-satellite applications. In this framework, we present THRawS, the first dataset composed of Sentinel-2 (S-2) raw data containing warm temperature hotspots (wildfires and volcanic eruptions). To foster the realisation of robust AI architectures, the dataset gathers data from all over the globe. Furthermore, we designed a custom methodology to identify events in raw data starting from the corresponding Level-1C (L1C) products. Indeed, given the availability of state-of-the-art algorithms for thermal anomalies detection on the L1C tiles, we detect such events on these latter and we then re-project them on the corresponding raw images. Additionally, to deal with unprocessed data, we devise a lightweight coarse coregisteration and georeferencing strategy. The developed dataset is comprehensive of more than 100 samples containing wildfires, volcanic eruptions, and event-free volcanic areas to enable both warm-events detection and general classification applications. Finally, we compare performances between the proposed coarse spatial coregistration technique and the SuperGlue Deep Neural Network method to highlight the different constraints in terms of timing and quality of spatial registration to minimise the spatial displacement error for a specific scene.