A parallel/counter-flow He II heat exchanger of total length 711.2 mm and flow area 2 mm × 4 mm has been designed, fabricated and tested under a variety of conditions in saturated He II. In the present paper, the experimentally measured temperature profiles for both parallel and counter-flow configurations are compared to a numerical model which is based on a combination of He II internal convection heat transfer and ordinary forced convection mechanisms. The numerical model used to fit the experimental results has one adjustable parameter, the heat transfer coefficient, h, which is dominated by the Kapitza conductance between He II and a solid surface. The results show that the value for h is independent of fluid velocity in agreement with the findings of previous studies. The He II heat exchanger investigated in this configuration exhibits an unusual temperature distribution not seen for classical fluids. For the parallel-flow case, the temperature profiles can cross at low fluid velocity, signalling a reversal of heat transfer. This result comes about because of the high heat conductivity of He II. At high velocities and in the counter-flow configuration, the behaviour is more similar to that commonly observed with classical, low thermal conductivity fluids. The features of the He II system that bring about these unique effects and a suggested approach to the design of such He II heat exchanger systems are presented.