The paper contains a simplified energy and exergy analysis of pumps and pipelines system integrated with Thermal Energy Storage (TES). The analysis was performed for a combined heat and power plant (CHP) supplying heat to the District Heating System (DHS). The energy and exergy efficiency for the Block Part of the Siekierki CHP Plant in Warsaw was estimated. CHP Plant Siekierki is the largest CHP plant in Poland and the second largest in Europe. The energy and exergy analysis was executed for the three different values of ambient temperature. It is according to operation of the plant in different seasons: winter season (the lowest ambient temperature Tex = −20 °C, i.e., design point conditions), the intermediate season (average ambient temperature Tex = 1 °C), and summer (average ambient temperature Tex = 15 °C). The presented results of the analysis make it possible to identify the places of the greatest exergy destruction in the pumps and pipelines system with TES, and thus give the opportunity to take necessary improvement actions. Detailed results of the energy-exergy analysis show that both the energy consumption and the rate of exergy destruction in relation to the operation of the pumps and pipelines system of the CHP plant with TES for the tank charging and discharging processes are low.