Buoyancy affects the horizontal wake far downstream of a heated or cooled body, especially a horizontal plate, in an indirect manner via the hydrostatic pressure perturbation. Plane (2D) flow at very large Reynolds and Péclet numbers is considered in the present paper. Both laminar and turbulent flows are analyzed. The equations of continuity, momentum, energy and, in case of turbulent flow, the balance of turbulent kinetic energy are written in boundary-layer approximation. Dimensionless variables are introduced, using the total heat flow from, or towards, the plate as a parameter. It turns out that the buoyancy effects in the momentum equations and in the turbulent kinetic energy balance, respectively, are of the same order of magnitude and can be chracterized by a Richardson number. To describe the far wake, asymptotic expansions for large distances from the plate are performed, leading to a set of ordinary differential equations for a self-similar flow field. According to previous work [1] there is an interaction between the wake and the potential flow. This effect is taken into account in the present analysis by applying Bernoulli’s equation as a boundary condition to the momentum equation of the wake. As the energy equation as well as the boundary conditions for the temperature perturbation are homogeneos, the solution of the temperature field contains a free coefficient, which is determined from the over-all energy balance. The results of the analysis are in remarkable contrast to the classical solutions for the wake flow without buoyancy [2]. In particular, driven by the hydrostaic pressure disturbance, the flow does not decay with increasing distance from the plate. Furhermore, the flow is governed by the total heat flow at the plate, whereas the effect of the drag force acting on the plate is negligible. The set of ordinary differential equations is solved numerically. For laminar flow, two kinds of solutions have been found. One of them describes a flow field containing a region of reversed flow. In case of turbulent flow the numerical solution requires the application of a turbulence model. The horizontal far wake is, by itself, an interesting problem of combined fluid and heat flow. In addition, a solution of the far-wake equations can be useful for dealing with the severe difficulties that are known to be associated with the downstream boundary conditions in numerical solutions of the full equations of motion for mixed convection flows. [1] Schneider, Proc. 3rd European Thermal Sci. Conf., Edizione ETS, Pisa (2000). Schneider, J. Fluid Mech., 529 (2005). Müllner, Schneider, Heat Mass Transfer, 46 (2010). [2] Schlichting & Gersten, Boundary-Layer Theory, 9th Ed., Springer (2017), pp. 187-190, 669-671.