Historical buildings account for a significant portion of the energy use of today’s building stock, and there are usually limited energy saving measures that can be applied due to antiquarian and esthetic restrictions. The purpose of this case study is to evaluate the use of the building structure of a historical stone building as a heating battery, i.e., to periodically store thermal energy in the building’s structures without physically changing them. The stored heat is later utilized at times of, e.g., high heat demand, to reduce peaking as well as overall heat supply. With the help of Artificial Intelligence and Convolutional Neural Network Deep Learning Modelling, heat supply to the building is controlled by weather forecasting and a binary calendarization of occupancy for the optimization of energy use and power demand under sustained comfortable indoor temperatures. The study performed indicates substantial savings in total (by approximately 30%) and in peaking energy (by approximately 20% based on daily peak powers) in the studied building and suggests that the method can be applied to other, similar cases.