The country's historical and artistic heritage represents its identity and history. Art cities are often influenced by different architectural styles, sometimes easily distinguishable, thanks to characteristic elements, other times less so, due to influences caused by transition periods from one style to another, or by interventions over the centuries. Artificial Intelligence in recent years, has proven to be a valuable tool in the field of image classification, given its capacity to yield robust solutions across diverse domains. However, its application in the cultural heritage building image classification context remains relatively unexplored. This paper presents a preliminary feasibility study aimed at investigating the potential of deep learning techniques for the classification of cultural heritage building images. The goal could be to build a solution that can recognize, given an image of a historic building, the architectural style, which could improve the experience of a tourist who wants to know more about the visited place's history. The paper examines the results obtained with different neural network architectures, exploiting the Transfer Learning technique, but also draws attention to the challenges of the domain. Overall, encouraging results (AUC 0.98 and F1-score equal to 94-95%), demonstrate the effectiveness of the techniques tested and show how AI can help the classification and preservation of cultural heritage building.