CF3I quasicontinuum (QC) states are analyzed in the framework used previously for SF6 in papers I and II of this series. The existence of a hierarchy of intramolecular couplings V(k), decreasing vs the number k of vibrational quanta exchanged, with an effective density of coupled states rho(k), is pointed out. The oscillator strength redistribution is described taking into account isolated resonances and perturbative redistribution associated to the lowest orders k, dissipative redistribution associated to higher orders, multiple transitions, and mode inhomogeneous spreading. Published homogeneous spectra of (CF3I)-C-12 and (CF3I)-C-13 at E = 19 000 cm-1, near the dissociation threshold, are reinvestigated in this framework and a new assignment of the resonances is proposed. Using fluorescence data at [E] = 3200 cm-1, an interpolation of the position and weight of the main resonances nu1, nu4, nu2 + nu3, 2nu5, in the frequency range 900-1200 cm-1, becomes possible. This interpolation allows to extract from IR multiphoton absorption data, at the laser frequency nu(L) = 1072 cm-1, an average Lorentzian half-width gammaBAR ([n]) vs the average number of photons absorbed (n). GammaBAR increases from 1 to 5 cm-1 for (n) varying from 5 to 10, and varies slowly around 4-5 cm-1 for 10 less-than-or-equal-to [n] less-than-or-equal-to 18. Finally, the onset of the QC, near E approximately 6000 cm-1, is explained using a modelization of the hierarchy V(k), rho(k), without arbitrary parameters, and an intramolecular relaxation time approximately 20 ps is predicted. This analysis leads to a very good agreement between the different sets of data concerning the CF3I molecule.