Variable working conditions of a double-tube counter-flow heat exchanger were analysed. During operation of the heat exchanger, the parameters (temperatures and mass flow rates) of both fluids at its inlet change, which leads to a change in its performance. Heat transfer effectiveness is commonly used to assess the heat exchanger performance, defined as the ratio of the actual to the maximum heat flow rate. In the present paper, the heat exchanger was considered to be a ‘black box’, and the aim was to investigate how the inlet parameters (temperatures and mass flow rates of both fluids) affect the outlet ones (temperatures of both fluids), and thus to attempt to introduce a new relation for the heat transfer effectiveness of a counter-flow heat exchanger as a function of only inlet parameters. Following the analysis, a relation for the heat transfer effectiveness as a function of inlet parameters with five constant coefficients was obtained. These coefficients depend on the heat exchanger geometry and on the properties of the heat transfer fluids; they are not general-purpose, but specific to a counter-flow heat exchanger. The form of the proposed relation for the heat transfer effectiveness of a counter-flow heat exchanger is not satisfactory as it involves five constant coefficients; therefore, a new approach was chosen, consisting in analysing a parameter defined as the ratio of the minimum to the actual arithmetic mean temperature difference. Using the parameter defined in this way, the relation for the heat transfer effectiveness of a counter-flow heat exchanger was obtained as a function of two parameters: the ratio of the heat capacity rates of both fluids, and *NTU*, with no constant coefficients. The proposed relations were verified against the data produced by a simulator of a double-tube counter-flow heat exchanger.