In this paper the exact solution of the heat transfer problem for generalized Newtonian flow between two infinite parallel plates is obtained by using the Fourier method and taking into account the viscous dissipation of the fluid. The original variable is proposed to expand the required function into a power series. The universal law is considered to describe a generalized Newtonian fluid. For example, an analytical solution is used to investigate the heat transfer problem for the flow of a rubber compound based on the synthetic isoprene rubber-3.