Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heated square cylinder in the unsteady cross-flow regime has been studied numerically by solving the relevant momentum and thermal energy equations using a finite-volume method for the range of conditions 0.7 ≤ Pr ≤ 50, 60 ≤ Re ≤ 160, and0.5 ≤ n ≤ 1.8. Over this range of Reynolds numbers, the flow is truly periodic for Newtonian and shear-thickening fluids, while in the case of shear-thinning fluids it becomes pseudo-periodic at high values of Re (≥140) and low values of n(≤0.6). This work is concerned only with the truly periodic regime and therefore the range of Reynolds number studied varies with the value of the power law index. The dependence of the local and average Nusselt number on the Reynolds number, Prandtl number, and power law index has been studied in detail. Broadly, shear-thinning (n<1) fluid behavior promotes heat transfer, whereas shear-thickening (n<1) impedes it. Further insights into the heat transfer phenomenon are provided in terms of isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power law index.