The authors calculate the reduced electronic thermal conductivity of a superconducting alloy containing paramagnetic impurities with local states within the gap. The Green function given by Shiba or Rusinov (1968-69) (for s wave scattering) is used which is appropriate for the case when the exchange scattering of a conduction electron from a magnetic impurity is strong. The temperature dependence of (K_s/K_n) for various impurity concentrations is shown and for a typical value of epsilon ₀ (=0.6; epsilon ₀ is a parameter which determines the strength of the conduction electron-impurity interaction). Significant deviations are found, from the theoretical results based on Abrikosov-Gor'kov theory ( epsilon ₀=1.0).