In recent years, most Russian regions have discovered that the branch of municipal heat supply is characterized by increased wear of the heat-generating and heat-network infrastructure, deficiency of investment projects, system organizational and economic problems, which exert impact on high-quality and reliable providing consumers of municipalities with utilities. In this regard, well-reasoned and accurately formulated municipal investment development strategies should be devised for solving the problems mentioned above. Investment strategies of municipal heat-energy systems are considered as basic and most important for municipalities, since questions of reconstruction (modernization) of the heat energy infrastructure are socially important. Thus, in the absence of an investment strategy, the investment processes in the communal heat supply industry will be slowed down, therefore, interest in financing will be significantly reduced, in addition, it can lead to investment inaction by the municipal administration, which in turn can lead to adverse consequences, including system crashes. Therefore, it is necessary to initiate an investment process in the municipal heat-energy system that will increase the reliability and quality of consumers' heat supply by updating worn-out fixed assets, and will also reduce the economically justified rate of heat supply organizations in the medium term. The problem in the paper is considered at the level of municipalities, with directions of investment strategy suggested for these entities. Further, these directions will be fundamental for the formation and development of an action program, with the mandatory account of investment planning. The scenarios for the development of the municipal heat-energy system are considered in the absence of an investment strategy both in the presence of an inter-tariff difference and in its absence. Also, graphical models for the functioning of the municipal heat-energy systems without the investment strategy of the two options for the development of municipal heat-energy systems (heat tariff dynamics), and an alternative graphic economic model for implementing the investment policy in the municipal heat-energy systems are presented. The analysis of the economic-mathematical model of the development of the energy complex of the municipality is made.