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Morphological features of the Mediterranean Sea basin have recently been precursors to a significant increase in the formation of extreme events, in relation to climate change effects. It happens very frequently that rotating air masses and the formation of mesoscale vortices can evolve into events with characteristics similar to large-scale tropical cyclones. Generally, they are less intense, with smaller size and duration; thus, they are called Medicanes, a short name for Mediterranean hurricanes, or tropical-like cyclones (TLCs). In this paper, we propose a new perspective for the study and analysis of cyclonic events, starting with data and images acquired from satellites and focusing on the diagnostics of the evolution of atmospheric parameters for these events. More precisely, satellite remote sensing techniques are employed to elaborate on different high spatial-resolution satellite images of the events at a given sensing time. Two case studies are examined, taking into account their development into Medicane stages: Ianos, which intensified in the Ionian Sea and reached the coast of Greece between 14 and 21 September 2020, and Apollo, which impacted Mediterranean latitudes with a long tracking from 24 October to 2 November 2021. For these events, 20 images were acquired from two different satellite sensors, onboard two low-Earth orbit (LEO) platforms, by deeply exploiting their thermal infrared (TIR) spectral channels. A useful extraction of significant physical information was carried out from every image, highlighting several atmospheric quantities, including temperature and altitude layers from the top of the cloud, vertical temperature gradient, atmospheric pressure field, and deep convection cloud. The diagnostics of the two events were investigated through the spatial scale capabilities of the instruments and the spatiotemporal evolution of the cyclones, including the comparison between satellite data and recording data from the BOLAM forecasting model. In addition, 384 images were extracted from the geostationary (GEO) satellite platform for the investigation of the events’ one-day structure intensification, by implementing time as the third dimension.