Due to decreasing supplies of fossil fuels and rising carbon dioxide concentrations in the atmosphere, milder and more environmentally friendly use of these resources are becoming more and more important. A more efficient use of energy sources and the development of renewable energy systems is only in conjunction with the storage of energy, over short and long periods of time, possible and useful. The temporal mismatch between energy supply and demand have to be balanced. In this paper, the thermodynamic processes in thermally stratified storages are studied. Occurring free conventions of the storage medium, can be converted into a one-dimensional heat conduction problem, by establishing an effective thermal conductivity. The Richardson number can be used, to assess the type of flow during a loading or unloading period. For sufficiently large values, an ideal plug flow for the entire storage can be assumed. The model equation results as the transport equation of thermal energy. Based on the findings, the development of numerical models, for the transient simulation of such storages, is carried out by using the finite volume method. With these models, a prediction of the temperature distribution and efficiency, as a function of time, can be made, for predefined conditions of operation. Integration of the storage model, for example in an already modeled thermal network or in a domestic heating system, makes it possible, to analyze the behavior of the overall system. Because of that, the anticipated cost reductions due to energy savings, can be contrasted with the investment costs of the real storage.