Effective Structural Health Monitoring (SHM) systems are essential for detecting potential damage to structures early, thereby ensuring their safety. Automated Operational Modal Analysis (AOMA) is a crucial technique for the vibration-based SHM. The increasing of available data sets coming from permanent monitoring evidences the need for reliable procedures to provide insights into their dynamic characteristics, such as natural frequencies, mode shapes, and damping ratios identified through accelerometric measurements under ambient vibration (unknown excitation). Therefore, automated approaches facilitate continuous and real-time structural integrity assessment, enhancing the ability to detect damage, assess performance, and ensure safety. However, environmental conditions, including temperature fluctuations, humidity, and varying wind speeds, can significantly influence the vibrational response of structures, potentially leading to inaccurate evaluation of the frequencies. To consider the effects of these factors, advanced signal processing techniques, and environmental condition normalization methods need to be employed on a large dataset, acquired by a long-term monitoring system, and processed by automated structural identification algorithms. This contribution describes the AOMA procedure developed for the continuous monitoring of the Exedra Hall, a renowned heritage building in the heart of Rome, within the complex of the Capitoline Museum, monitored by a permanent system composed of six MEMS accelerometers, continuously operating since the end of July 2023. The automated modal identification procedure integrates stochastic subspace identification, data clustering, and outlier removal techniques to automatically detect, classify, and track natural frequencies over time. The AOMA results obtained for one year of measurements are presented in this contribution, and preliminary remarks on the influence of environmental factors are outlined.