A simple criterion for screening experimental data on turbulent heat transfer in vertical tubes to identify those not significantly influenced by buoyancy was proposed by the author many years ago and found to work quite well for water and air at normal pressures. However, it was recognized even then that the ideas on which the criterion was based were too simplistic to be suitable for use in the case of fluids at supercritical pressure. With the passage of time and tremendous advancement in data processing capability using present-day computers, it is now possible to contemplate adopting a refined approach specifically designed to be suitable for such fluids. The present paper describes a semi-empirical model of buoyancy-influenced heat transfer to fluids at supercritical pressure, which takes careful account of nonuniformity of fluid properties. It provides a criterion for determining the conditions under which buoyancy influences are negligibly small. Thus, the extensive databases now available on heat transfer to fluids at supercritical pressure can be reliably screened to eliminate those affected by such influences. Then, the many correlation equations that have been proposed for forced convection heat transfer can be evaluated in a reliable manner. These equations mostly relate Nusselt number to Reynolds number, Prandtl number, and simple property ratio correction terms. Thus, they should be evaluated using only experimental data that are definitely not influenced by buoyancy. A further outcome of the present paper is that it might now prove possible to correlate the buoyancy-influenced data in such databases and fit the equation for mixed convection heat transfer yielded by the model to the correlated data. If this can be done, it will represent a major advancement in terms of providing thermal analysts with a valuable new tool.