The model of the perfect continuous counterflow heat exchanger introduced by Frossatietal. to describe the performance of dilution refrigerators is solved rigorously with the proper boundary condition. Unlike the original solution by Frossatietal., the present solution gives the refrigerator cooling power which is in good agreement with experimental data over the entire temperature range. The analysis of the cooling power using the present result allows more detailed evaluation of the refrigerator performance than has been possible with the analysis of the base temperature. An approximate expression for the cooling power is discussed which simplifies the prediction of the cooling rate of a large thermal load such as a copper nuclear‐demagnetization stage.