Tertiary buildings could be an important lever to meet the goals necessitated by the energy transition. The availability of high-quality datasets from this sector will be a crucial enabler in meeting these goals by developing and testing new energy management approaches in the buildings. In this paper, we present the thermal energy datasets available and published online for the PREDIS-MHI zone of the GreEn-ER building, a tertiary building with more than a thousand sensors used for research, teaching, and administrative activities in Grenoble. PREDIS-MHI platform is a net-zero sub-section that is energetically isolated from the rest of the building. Its data has been used in a wide range of applications from indoor temperature forecasting, thermal simulation calibration, and even occupant comfort experiments