The second law of thermodynamics is applied to evaluate the influence of entropy generation on the performances of a cold heat exchanger of an experimental Stirling refrigeration machine by means of three factors: the entropy generation rate N S , the irreversibility distribution ratio ? and the Bejan number B e | N S based on a dimensionless entropy ratio that we introduced. These factors are investigated as functions of characteristic dimensions of the heat exchanger (hydraulic diameter and length), coolant mass flow and cold gas temperature. We have demonstrated the role of these factors on the thermal and fluid friction irreversibilities. The conclusions are derived from the behavior of the entropy generation factors concerning the heat transfer and fluid friction characteristics of a double-pipe type heat exchanger crossed by a coolant liquid (55/45 by mass ethylene glycol/water mixture) in the temperature range 240 K < TC < 300 K. The mathematical model of entropy generation includes experimental measurements of pressures, temperatures and coolant mass flow, and the characteristic dimensions of the heat exchanger. A large characteristic length and small hydraulic diameter generate large entropy production, especially at a low mean temperature, because the high value of the coolant liquid viscosity increases the fluid frictions. The model and experiments showed the dominance of heat transfer over viscous friction in the cold heat exchanger and B e | N S → 1 and ? → 0 for mass flow rates m ? → 0.1 kg.s−1.