The generalized integral transform technique (GITT) is employed in the solution of the boundary layer equations,in simultaneously developing laminar flow of power-law non-Newtonian fluids within a parallel plates channel. In the modeling of the related momentum and energy equations within the range of validity of the boundary layer equations, a streamfunction formulation is employed which offers a better computational performance than the primitive-variables formulation. Numerical results for the bulk temperature and Nusselt numbers are established at different axial positions along the channel and for various power-law indices, and critical comparisons with previously reported works in the literature are also performed.