Aesthetic emotions are elicited by different sensory impressions generated by music, visual arts, literature, theater, film, or nature scenes. Recently, the AESTHEMOS scale has been developed to facilitate the empirical assessment of such emotions. In this article we report a semantic profile analysis of aesthetic emotion terms that had been used for the development of this scale, using the GRID approach. This method consists of obtaining ratings of emotion terms on a set of meaning facets (features) which represent five components of the emotion process (appraisal, bodily reactions, action tendencies, expression, and feelings). The aims here were (a) to determine the dimensionality of the GRID features when applied to aesthetic emotions and compare it to published results for emotion terms in general, and (b) to examine the internal organization of the domain of aesthetic emotion terms in order to identify salient clusters of these items based on the similarity of their feature profiles on the GRID. Exploratory Principal Component Analyses suggest a four-dimensional structure of the semantic space consisting of valence, power, arousal, and novelty, converging with earlier GRID studies on large sets of standard emotion terms. Using cluster analyses, 15 clusters of aesthetic emotion terms with similar GRID feature profiles were identified, revealing the internal organization of the aesthetic emotion terms domain and meaningful subgroups of aesthetic emotions. While replication for further languages is required, these findings provide a solid basis for further research and methodological development in the realm of aesthetic emotions.