In the combustion community there seems to be a persistent view that Ludwig-Soret (L-S) (thermally driven, non-Fickian) species diffusion will only be important for low molecular weight species, such as H and H-2 in H-2/air flames. In the present paper we mobilize and extend some relevant research which, among other things, proves this particular viewpoint to be untrustworthy, replacing it with more robust and readily used criteria tailored to high molecular weight (Sc > 1) species. As an immediate corollary of the results presented/discussed here, many previous "L-S-free" theoretical studies of (large or small) "Lewis number effects in combustion" must be re-examined and extended since "extreme" nonunity Lewis number effects and significant L-S transport effects will frequently "go together." Often, lack of direct experimental information about the relevant thermal diffusion factor alpha (T), or even complexity of the underlying kinetic theory expressions for alpha (T), are used to "justify" neglecting L-S species transport. To overcome this we suggest and exploit two remarkably simple but rational approximate methods to estimate alpha (T) for "heavy" species via the already familiar Schmidt number nu (A)/D-BA, in the ideal gas, high temperature limit. We also provide, as a corollary, simple but rational correlations/estimates for anticipating the simultaneous consequences of Fick and Ludwig-Soret diffusional transport, including: appreciable modifications of the recovery factor for mainstream chemical energy (Rosner [1]) in surface-catalyzed combustion. Using instructive examples for nonpremixed and surface-catalyzed combustion, we demonstrate the importance of L-S transport for heavy fuel vapor species (even the normal paraffins CnH2n+2 smaller than eicosane (n = 20; Table 1), as well as for flame intermediates (including soot precursors, such as polycyclic aromatic hydrocarbons (PAHs) up to coronene (C24H12; Table 2). We conclude that it is not only bona fide soot particles that are appreciably influenced by "thermophoresis" in such laminar diffusion flames-even for coronene we estimate (Table 2) that the dimensionless "thermophoretic diffusivity": alpha D-T(BA)/nu (g), is already about 0.47, not far from the particle-limit value of 0.5385. Put another way, in combustion applications the L-S effect, while known to be important for diffusion flames involving H(g) and H-2(g), does not "disappear" for heavier vapors, only to "suddenly'' reappear for bona-fide nanoparticles (e.g., "soot")!