A mathematical model is developed to study the performance of a parallel-flow heat exchanger in which both fluid streams are interacting thermally with the surroundings. The fluid temperatures are found to be dependent on the magnitude of the ambient temperature relative to fluid inlet temperatures, the ratios of conductances between the fluids and the ambient and the interfluid conductance, the ratio of minimum to maximum fluid capacities, and the number of transfer units, NTU, for the heat exchanger. Two heat exchanger effectiveness criteria, one each for the hot and cold fluids, are used to study performance. The effectiveness is found to be adversely affected by increasing conductance ratios, increasing NTU, and increasing temperature difference between the ambient and the fluid of interest. For very high values of the conductance ratios, the heat exchanger will not perform as expected and both fluid temperatures will approach that of the ambient. The parallel-flow arrangement is compared to counterflow and is found to be less effective under the external heat transfer condition.