The present study attempts to explore the effects of viscous dissipation on the heat transfer characteristics in the conduction limit for the Couette flow of power-law fluids between asymmetrically heated parallel plates. Here, two types of power-law fluids are considered (e.g., the pseudoplastic (n < 1) and dilatants (n > 1)) along with the special case of n = 1 (i.e., the Newtonian fluid). Utilizing the assumptions routinely employed in the literature, a semianalytical framework is devised to explore the effects of viscous dissipation on the limiting heat transfer characteristics. The shear produced by the movement of the upper plate in the dynamics of flow is emphasized; hence, a weak pressure gradient in the flow field is considered, which could otherwise create a complicated situation in the derivation of velocity distribution for the non-Newtonian Couette flows considered in this study. Despite the effect of viscous dissipation on the limiting heat transfer, the effect of asymmetrical wall heating on the same is shown for all the cases under consideration. Using these results, the possibilities of obtaining different temperature profiles and the variation of Nusselt number for different types of power-law fluid are aptly highlighted in view of the energy balance and analysis of the second-law of thermodynamics.