Transient temperature response of a parallel-flow three-fluid heat exchanger with the thermal capacitance of the walls and the longitudinal heat conduction through the walls is investigated numerically, by the implicit MacCormack method, for a step change in flow rate of one fluid. The impact of thermal properties of the walls on temperature field is examined. The results of calculations show that as the thermal diffusivity of the walls decreases, the effect of the walls increases.