This work proposes a new unsupervised method to evaluate the behavior of urban green areas in the presence of heatwave scenarios by analyzing three indices extracted from satellite data: the Normalized Difference Vegetation Index (NDVI), the Normalized Difference Moisture Index (NDMI), and Land Surface Temperature (LST). The aim of this research is to analyze the behavior of urban vegetation types during heatwaves through the analysis of these three indices. To evaluate how these indices characterize urban green areas during heatwaves, an unsupervised classification method of the three indices is proposed that uses the Elbow method to determine the optimal number of classes and the Jenks classification algorithm. Each class is assigned a Gaussian fuzzy set and the green urban areas are classified using zonal statistics operators. The membership degree of the corresponding fuzzy set is calculated to assess the reliability of the classification. Finally, for each type of greenery, the frequencies of types of green areas belonging to NDVI, NDMI, and LST classes are analyzed to evaluate their behavior during heatwaves. The framework was tested in an urban area consisting of the city of Naples (Italy). The results show that some types of greenery, such as deciduous forests and olive groves, are more efficient, in terms of health status and cooling effect, than other types of urban green areas during heatwaves; they are classified with NDVI and NDMI values of mainly High and Medium High, and maximum LST values of Medium Low. Conversely, uncultivated areas show critical behaviors during heatwaves; they are classified with maximum NDVI and NDMI values of Medium Low and maximum LST values of Medium High. The research results represent a support to urban planners and local municipalities in designing effective strategies and nature-based solutions to deal with heat waves in urban settlements.