The article is dedicated to the safety assessment of mixed storage of irradiated graphite and other types of radioactive waste accumulated during the operation of uranium-graphite reactors. The analysis of heat release processes inside storages containing irradiated nuclear graphite, representing a potential hazard due to the possible heating and, accordingly, the release of long-lived radionuclides during oxidation was carried out. The following factors were considered as the main factors that can lead to an increase in the temperature inside the storage facility: corrosion of metallic radioactive waste, the presence of fuel fragments, and also the random exposure of irradiated graphite to local sources of thermal energy (spark, etc.). It was noted in the work that the combined or separate influence of some factors can lead to an increase in the temperature of the onset of the initiation of Wigner energy release in graphite radwaste (Tin ≈ 90–100°C for the “Worst-case” graphite). The model of heat generation in the storage was developed based on the analysis of the features of graphite radioactive waste storage and Wigner energy release. The layered location of different types of waste (graphite and aluminum) and the local character of the distribution of heat sources were adopted in this model. The greatest heating is achieved if graphite radioactive waste is located near the concrete walls of the storage facility, as well as in direct contact with irradiated aluminum radioactive waste, which was shown in this paper.