In this work, the Non-Oberbeck-Boussinesq effects combined with the power-law behavior of the fluid has been numerically investigated to elucidate the extent and significance of temperature-dependent fluid properties. In this context, an isothermal horizontal cylinder is taken in to account for natural convection to unconfined shearthinning (0.3 ≤ n ≤ 1) power-law fluids with practical characteristic temperature difference ΔT of 20K (where the Oberbeck-Boussinesq (OB) approximation fails). The powerful computational fluid dynamics (CFD) solver ANSYS-Fluent has been implemented to perform the finitevolume method (FVM) based numerical computations for the present work. This paper outlines the relative importance of temperature-dependent flow consistency index (C) and temperature-dependent thermal expansion coefficient (α) on both momentum and heat transfer characteristics. Effects of both individual temperature dependency of thermal expansion coefficient (α-NOB) and consistency index (C-NOB) and combined temperature dependency (NOB) on average Nu changes are also expounded in this study. At the extreme value of temperature difference, ΔT = 20K, the NOB effect augments the average Nu by 33% at n = 0.3, which reduced to 17% at n = 1 (Newtonian case), with reference to the OB solutions.