In this work is proposed a new unsupervised method to evaluate the behavior of urban green areas in presence of heatwave scenarios analyzing the NDVI, NDMI and LST satellite data. To evaluate how these three indices characterize urban green areas during periods of heat waves, a reclassification of the data raster of each index is carried out. Rather than using standard classifications of the three indices, an unsupervised classification approach is proposed that uses the Elbow method to determine the optimal number of classes and the Jenks thematic classification method. Each class is assigned a Gaussian fuzzy set with means and standard deviations equal to that of the associated thematic class. The green urban areas are classified using zonal statistics operators and the degree of membership in the corresponding fuzzy set is used to assess the reliability of the classification. Finally, for each type of greenery the frequencies of belonging to the NDVI, NDMI and LST classes are analyzed to evaluate the behavior of the type of urban greenery 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 not very vulnerable to heatwave scenarios, unlike uncultivated areas which, instead, show critical behaviors during heatwaves.