The current numerical study focuses on the feasibility of furnishing thermal comfort in a structure, by using paraffin wax stored on a plate below the ceiling in a multi-storey building. The method is aimed to reduce energy demands at the increasing thermal loads. In summer, in daytime, walls of the building are exposed to the ambient thermal load, and heat transferred inside is absorbed by the melting wax. The study is numerical. It relates to temperature variations outside and inside, coupled with heat conduction and accumulation in walls, with radiation between the surfaces, with natural convection of air inside and melting of the wax at the ceiling. Fins spacing on the storage plate, visualization of the melting process, and its parametric investigation provide an insight into the physical phenomena. Temperature and flow fields were investigated for 3 mm and 12 mm thick layers of wax. At the specified conditions of the present study a 3 mm layer provides thermal comfort for most of the day, while a 6 mm layer may suffice for the entire day. Fluent 6.3 software was used in the computations.