The displacement ventilation method of providing quality indoor air relies on the use of buoyant plumes generated by discrete heat sources. A number of practical displacement ventilation techniques are based on the model of a buoyant plume generated by a point heat source. Such a model has a number of intrinsic flaws. In particular, it is inapplicable in a finite region above the source. Furthermore, the solutions for the point source, when obtained for turbulent flow, require empirical inputs for their completion. These limitations have motivated the present numerical simulation. Consideration is given here to the turbulent buoyant plume generated by a heated finite sphere. In the limit of a vanishing radius, the sphere reduces to a point source. The numerical simulations are based on a model free of simplifying assumptions, aside from axisymmetry. The resulting numerical solutions have quantified the zone in which the point-source solutions are valid. Furthermore, the virtual origins needed to give meaning to the point-source solutions have been determined. This information serves to elevate the point-source solutions to practical relevance. In themselves, the numerical solutions demonstrate that at sufficient heights above the heated sphere, the velocity and temperature profiles in the buoyant plume become self-similar when plotted in terms of a similarity variable.