Conventionally, district heating networks have been developed with a centralized logic, with large generation units designed to provide space heating to distributed users. Some networks have already evolved to a stage in which multiple generation units are distributed throughout the network and are supplying heat from different sources and with different schedules. ICT technologies can be the basis for a live optimization of the network, which can be implemented by minimizing energy supply cost for the users or minimizing greenhouse gases emissions. This paper presents an analysis of the potential effects of including distributed heat storage units to an existing DH network, as the first step toward opening the interaction with users. The results show the limited effect of the demand profile variation in comparison with the potential benefits of optimization strategies against the current operation of the case study under analysis, the main reason being the good flexibility of the available heat generation units. Thus, the installation of distributed storage units should be preferred in DH networks characterized by a large share of non-flexible generation options, such as solar energy or waste heat from industries, or where the energy prices show large variations over the day.