Extensive numerical results are reported on the steady laminar natural convection in power-law fluids from a heated horizontal cylinder of square cross-section tilted by 45° from the direction of gravity thereby resulting in an upward flow due to density difference. The governing differential equations describing the fluid flow and heat transfer have been solved numerically over wide ranges of dimensionless parameters, namely, Grashof number (10 ≤ Gr ≤ 105), Prandtl number (0.72 ≤ Pr ≤ 100) and power-law index (0.3 ≤ n ≤ 1.8). The detailed flow and temperature fields in the proximity of the cylinder surface are visualized in terms of streamline and isotherm profiles respectively. Further insights are provided in terms of the distribution of the local Nusselt number along the cylinder surface together with its average value. Broadly speaking, over the ranges of conditions spanned herein, the flow remains attached to the surface of the cylinder. Furthermore, all else being equal, shear-thinning fluid behaviour promotes heat transfer whereas shear-thickening somewhat impedes it. Indeed, it is possible to enhance the rate of heat transfer by up to 100% in shear-thinning fluids in comparison to the Newtonian fluids under appropriate conditions. The inclination of the cylinder (α = 45°) also enhances the rate of heat transfer in comparison to an untilted cylinder. Finally, the heat transfer results are correlated by using a simple analytical form which facilitates interpolation of the present results for intermediate values of the pertinent dimensionless parameters.