Convenient and accurate expressions for the radiative flux deep inside an arbitrarily shaped, differentially moving, optically thick medium are derived. Spectral lines are included either ina deterministic way or stochastically by assuming a Poisson point process. It is shown that the lines lead to decreasing fluxes when in the medium the absolute value of the velocity gradient is increased. The flux vector needs no longer to be parallel to the temperature gradient in contrast to the radiative acceleration, which to a very good approximation is not influenced by lines. Formulae for the corresponding mean values of the opacity are presented and discussed.