An elementary “hydrodynamic/Brownian motion” model of the thermal diffusivity D_T of a class of “ideal” binary liquid mixtures, previously proposed by the author and his then collaborator, Bielenberg, is given a more transparent derivation than originally, exposing thereby the strictly kinematic-hydrodynamic nature of an important class of thermodiffusion separation phenomena. Moreover, it is argued that the solvent's thermometric diffusivity α appearing in that theory as one of the two fundamental parameters governing D_T should be replaced by an O(1) multiple of the solvent's (isothermal) self-diffusivity, D_S. The resulting formula for the thermal diffusion coefficient, D_T=λD_Sβ, with β the solvent's thermal expansivity and λ a term of O(1) dependent only upon the properties of the solvent, but not of the solute, is, on the basis of its derivation, presumably valid only under certain idealized, albeit well-defined, circumstances. This occurs when the solute molecules are: (i) large compared with those of the solvent; (ii) present only in small proportions relative to those of the solvent; and (iii) physicochemically inert relative to the solvent. When these conditions are met, the resulting thermal diffusivity of the mixture is, in theory, independent of any and all properties of the solute. Moreover, because β is algebraically-signed, the thermal diffusivity can either by positive or negative, according as the solvent expands or contracts upon being heated. This formula for D_T is compared with experimental data available for selected binary liquid mixtures. Reasonable agreement is found in almost all circumstances, with λ near unity to within a factor of about two or three, especially when the solute-solvent mixture properties closely approximate those where agreement would be expected, and conversely. Finally, it is pointed out that for the trio of idealized circumstances described, the formula D_T=λD_sβ is equally credible for gases. Here, based on gas-kinetic theory, it is possible to furnish the theoretical value of λ. Overall, while spanning a range of about five orders of magnitude, the D_T values given by this elementary formula are shown to apply with reasonable accuracy to: (i) liquids (including circumstances for which D_T is negative) as well as gases; (ii) all combinations of solvents and solutes tested (the latter including, for example, polymer molecules and metallic colloidal particles); and (iii) all sizes of solute molecules, from angstroms to submicrons.