The momentum and forced-convection heat-transfer characteristics for an incompressible and steady flow of power-law liquids past a square cylinder in a plane channel have been analyzed numerically. The momentum and energy equations have been solved using a finite-difference method for a range of rheological and kinematic conditions as follows: power-law index, n = 0.5-1.4, thereby covering both shear-thinning and shear-thickening behavior; Reynolds number, Re = 5-40; and Peclet number, Pe = 5-400. However, all computations have been performed for one blockage ratio b/2h = 1/8. Furthermore, the role of the type of thermal boundary condition, i.e., the constant heat flux and the isothermal surface, on the rate of heat transfer has also been studied. Overall, when the drag coefficient and Nusselt number are normalized using the corresponding Newtonian values, these ratios show only marginal additional dependences on the flow behavior index. The shear thinning not only reduces the size of the wake region but also delays the wake formation, and shear thickening shows the opposite effect on wake formation, etc.