In this work, the effects of aspect ratio and shear-dependent viscosity on the laminar free convection heat transfer from a heated spheroid immersed in unbounded quiescent power-law fluids have been investigated. In particular, the coupled momentum and energy equations have been solved numerically over the following ranges of the pertinent governing parameters: Grashof number, 10 <= Gr <= 10(5); Prandtl number, 0.72 <= Pr <= 100; power-law index, 0.3 <= n <= 1.5 and aspect ratio, 0.2 <= e <= 5. Detailed structures of the flow and temperature fields in the vicinity of the spheroid are visualized in terms of the streamline and isotherm patterns, whereas the gross flow and heat transfer phenomena are resolved in terms of the local Nusselt number and its surface averaged value and drag coefficient (C-D). Broadly speaking, shear-thinning fluid behaviour (n < 1) facilitates heat transfer whereas shear-thickening (n > 1) impedes it in comparison to that seen in Newtonian fluids (n = 1) under otherwise identical conditions. At fixed values of the Grashof number (Gr), Prandtl number (Pr) and power-law index (n), the value of Nusselt number gradually increases as the spheroid shape progressively passes from the oblate (e > 1) to the prolate (e < 1) configurations via the spherical shape (e = 1). The reverse trend occurs, however, for the drag coefficient (C-D). Finally, the present values of the average Nusselt number and drag coefficient are correlated using a simple analytical form based on a general composite parameter proposed for power-law fluids. The paper is concluded by presenting some comparisons with the limited previous analytical and experimental results available in the literature which are limited to Newtonian fluids. (C) 2014 Elsevier Ltd. All rights reserved.