Early fault detection and diagnosis in heating, ventilation and air conditioning (HVAC) systems may reduce the damage of equipment, improving the reliability and safety of smart buildings, generating social and economic benefits. Data models for fault detection and diagnosis are increasingly used for extracting knowledge in the supervisory tasks. This article proposes an autonomic cycle of data analysis tasks (ACODAT) for the supervision of the building’s HVAC systems. Data analysis tasks incorporate data mining models for extracting knowledge from the system monitoring, analyzing abnormal situations and automatically identifying and taking corrective actions. This article shows a case study of a real building’s HVAC system, for the supervision with our ACODAT, where the HVAC subsystems have been installed over the years, providing a good example of a heterogeneous facility. The proposed supervisory functionality of the HVAC system is capable of detecting deviations, such as faults or gradual increment of energy consumption in similar working conditions. The case study shows this capability of the supervisory autonomic cycle, usually a key objective for smart buildings.