It is well known that scattering leads to dispersion. The two constitute, respectively, the imaginary and the real parts of the index of refraction, which are connected by Kramers-Kronig relations. The effects of scattering-induced dispersion on the thermal conductivity have been ignored heretofore. It is shown that for strongly interacting and/or highly concentrated systems the additional dispersion will make a significant difference to the calculated thermal conductivity. The conductivity including dispersion has been calculated and compared with experimental results for solid 3He-4He mixtures, and for the KCl:CN- system. In order to conform to the dispersion relations for the latter, it was necessary to use a model for which the scattering cross section varied as the phonon frequency to the fourth power, in the low-frequency limit. For a multilevel system the scattering cross section must depend on the occupation of the levels. This leads to a temperature dependence of the cross section. Expressions for the cross section appropriate to multilevel systems were derived, and employed in calculating the thermal conductivity of KCl:CN-. These expressions are similar to those obtained by numerous investigators for spin systems.