We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.