The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically. In particular, the impact of nanofluids, composed of water and Al₂O₃, TiO₂, and Cu nanoparticles, on heat transfer enhancement is examined. The aim of this research is also to analyze the influence of different parameters, including the Rayleigh number (Ra = 104 − 106), nanoparticle volume fraction (φ = 0% − 20%), non-Newtonian power-law indexes (n = 0.6 − 1.4), and fin dimensions (Ar = 0.3, 0.5, and 0.7). Streamlines and isotherms are used to depict flow and related heat transfer characteristics. Results indicate that thermal performance improves with increasing Rayleigh number, regardless of the nanoparticle type or nanofluid rheological behavior. This suggests that the buoyancy force has a significant impact on heat transfer, particularly near the heat source. The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃ and TiO₂. Moreover, the average Nusselt numbers for power-law nanofluids with n < 1 (n > 1) are greater (smaller) than for Newtonian fluids due to the decrease (increase) in viscosity with increasing (decreasing) shear rate, at the same values of Rayleigh number Ra owing to the amplification (attenuation) of the convective transfer. Notably, the most substantial enhancement is observed with Cu–water shear-thinning nanofluid, where the Nusselt number increases by 136% when changing from Newtonian to shear thinning behavior and by 154.9% when adding 16% nanoparticle volume fraction. Moreover, an even larger increase of 57% in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.