In many applications, convective heat transfer is coupled with conductive and radiative heat transfer which generate temperature gradients along the walls and may greatly affect natural convective heat transfer. In this paper, the influence of the non-uniformity of wall temperature on the heat transfer by natural convection along a vertical plate having a linearly distributed temperature (characterized by the slope S) is pointed out. Heat transfer correlations giving Nusselt number vs Rayleigh number and S for both laminar and turbulent flows are obtained.