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In this paper, district heating is described and its operation process is considered in varying operation conditions over time. Taking into account the ordered thermal power which affects the amount of heat supply to consumers, the system operation states are introduced. Heat supply to consumers is carried out by means of a heat-carrying agent having the necessary parameters: required quantity, temperature and pressure, in a specific location, under certain operational conditions and timeframe. To model the system operation process and describe the changes between the operation states the semi-Markov process is applied. The identification of the district heating operation process is performed on the basis of real operational data obtained from the District Heating Company in the city of Rzeszow. Using the data and considering the specific character of the system, the main characteristics describing the safety of heat supply to consumers were determined. [ABSTRACT FROM AUTHOR]