The paper considers a single-buyer model of the oligopoly heat market. A mathematical model of the heat market is developed. It allows us to take into consideration economic and technical aspects of heating system’s operation. The problem of the determination of the Cournot-Nash equilibrium in the heat market at a linear demand function and nonlinear costs of heat sources is investigated and solved. To search for the Cournot-Nash market equilibrium we suggest an iterative algorithm based on step-by-step optimization of heat volumes produced by heat sources. The developed model was applied to perform practical studies on a heating system with two heat sources