The steady two-dimensional mixed-convection flow past a heated or cooled horizontal plate of finite length is analysed for large Péclet numbers and weak buoyancy effects. The plate is assumed to be aligned with the free stream. It is shown that the hydrostatic pressure jump across the wake, combined with the Kutta condition, gives rise to a potential flow that can be determined by distributing vortices in the wake as well as in the plate. Solutions in closed form are obtained for two cases, i.e. laminar flow of a fluid with very small Prandtl number and turbulent flow. As a result, a lift force opposite to the buoyancy force and a tangential force opposite to the viscous drag force are found. For the case of laminar flow of a fluid with very small Prandtl number, closed-form solutions are also obtained for the temperature distribution and the heat transfer rate, respectively.