A. mathematical model for the flow and heat transfer in an accelerating liquid film of a non-Newtonian power-law fluid is presented. The thermal boundary layer equation permits exact similarity solutions only in the particular case when the power-law index n is equal to unity, i.e. for Newtonian films. To this end, the heat transfer problem is solved by means of a local nonsimilarity approach with n and local Prandtl number Pr-x being the only parameters. A critical Prandtl number Pr-x* is introduced, which is a monotonically increasing function of n. The nonsimilar heat transfer problem is integrated numerically for several parameter combinations in the ranges 0.2 less than or equal to n less than or equal to 2.0 and 0.001 less than or equal to Pr-x less than or equal to 1000 and the calculations for n = 1 compared favourably with earlier results for Newtonian liquid films. For high Prandtl numbers, the temperature gradient at the wall is controlled by the wall gradient of the streamwise velocity component, which is practically independent of n for dilatant fluids (n > 1.0) but increases significantly with increasing pseudoplasticity (n < 1.0). For Pr-x much less than 1, on the other hand, the wall gradient of the temperature field increases slowly with n and this modest variation is ascribed to the displacement effect caused by the presence of the momentum boundary layer. Curve-fit formulas far the temperature gradient at the wall are provided in order to facilitate rapid and yet accurate estimates of the local heat transfer coefficient and the Nusselt number.