Steady free convection laminar boundary-layer flow about a heated vertical cone immersed in a quiescent power-law fluid is investigated. Surface temperature is assumed to have a power-law variation with the distance. Similarity solutions are obtained numerically for the boundary-layer velocity and temperature profiles, Magnitudes of the velocity and temperature profiles are found to decrease with increasing values of the flow behaviour index and the surface temperature exponent. The effects of flow behaviour index and the generalized Prandtl number on the surface shear stress and heat flux are determined. Copyright (C) 2001 John Wiley & Sons, Ltd.