Combining numerics and asymptotic methods in the limit of large Boltzmann and Zel＇dovich (Ze) numbers, we study how the burning speed (U) of rich, adiabatic dust-flames is affected by gradient (e.g. turbulent-) transport of heat and species. Depending on the gradient-to-radiative diffusivity ratio eta (a Planck number) evaluated in the high-temperature region, two asymptotic regimes are identified and analyzed: eta = O(Ze(-1)) leads to U(eta) < U(0), due to reactant spreading by diffusion, whereas eta = O(1) and large enough ultimately yields the opposite trend, due to enhanced overall conductive effects. An analytical composite expression of U(eta,Ze) which encompasses both effects is provided and allows one to estimate the minimum burning speed; the latter decreases with Ze increasing.