A heat management system include including application of phase change materials (PCM). A heat or cold storage multistage tower has a housing with a multistage system of flat rigid container. A significant fraction of internal space of each container is filled with PCM; these containers are fabricated from ceramics, glass, glass ceramics or sulfur concrete. Another version of the heat or cold storage tower is based on application of multi-channel blocks from ceramics, glass, glass ceramics or sulfur concrete; the parallel internal vertical channels of the blocks are open and sealed at their bottoms alternatively, and the channels with the sealed bottoms are filled partially with PCM. The tower achieves effective heat transfer between a heat transfer fluid (HTF) and PCM in the processes of charging and discharging of the containers with heat or cold.