Analysis of convection flow and heat transfer of a viscous heat-generating fluid near an infinite vertical stretching surface is carried out. The effects of free convection and the presence of heat generation/absorption on the flow and heat transfer characteristics are considered. The equations of conservation of momentum, mass, and energy, which govern the flow and heat transfer problem, are solved numerically by using a variable order, variable step size finite-difference method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of free convection on the flow and heat transfer characteristics.