We present detailed calculations on the basis of our recent proposal for simultaneous cooling of the rotational, vibrational and external molecular degrees of freedom . In this method, the molecular ro-vibronic states are coupled by an intense laser and an optical cavity via coherent Raman processes enhanced by the strong coupling with the cavity modes. For a prototype system, OH, we showed that the translational motion is cooled to a few μK and the molecule is brought to the internal ground state in about a second. Here, we investigate numerically the dependence of the cooling scheme on the molecular polarizability, selecting NO as a second example. Furthermore, we demonstrate the general applicability of the proposed cooling scheme to initially vibrationally and rotationally hot molecular systems.