A hot stream of a very viscous fluid, such as a polymer, may be cooled in a heal exchanger consisting of multiple parallel passages. However, if a quite uniform temperature distribution is desired in the exit stream, the fluid flowing through each of the passages must be cooled to very nearly the same temperature. An analytical treatment of heat transfer and pressure drop in viscous flow between parallel plates during cooling reveals the operating conditions and passage geometry required to achieve this goal. Solution of the equation obtained depends only on the physical properties of the fluid and the cooler geometry. Non-Newtonian behavior of the fluid is approximated by a power-law function. A unique type of heat exchanger was designed on the basis of this analysis.