The article describes detailed measurements of indoor environmental parameters in a multiapartment housing block located in Milan, Italy, which has recently undergone a deep energy retrofit and is used as a thermal battery during the winter season. Two datasets are provided: one refers to a series of experimental tests conducted by the authors in an unoccupied flat, in which the thermal capacity of the building mass is exploited to act as an energy storage. The dataset reports, with a time step of 10 min, measurements of air temperature, globe temperature and surface temperatures in the analyzed room and data characterizing the adjacent spaces and the outdoor conditions. The second set of data refers to the air temperature monitoring carried out continuously in all the apartments of the apartment block, and hence also during two unplanned heating power outages. The analyzed data show the role of deep renovations in extending the time over which a building can remain in the thermal comfort range after an energy interruption and thus highlight the potential role of retrofitted buildings in delivering energy flexibility services to related stakeholders, such as the occupants, the building manager, the grid operator, and others. Furthermore, the dataset can be used to calibrate an energy simulation model to investigate different demand-side flexibility strategies and evaluate thermal safety under extreme weather events.