The statistical associating fluid theory (SAFT) was used to predict the thermal conductivity of multicomponent mixtures, through the concept of residual entropy scaling. The concept suggests that the transport properties of fluid, when reduced using an appropriate reference, can solely be described through a monovariant dependence on residual entropy. The thermal conductivity of an ideal gas mixture based on the Chapman and Cowling approximation with a Mason and Saxena mixing rule, was used as a reference for entropy scaling. The proposed model was applied to fully predict the thermal conductivity of refrigerant blends containing hydrocarbons, hydrofluorocarbons, hydrofluoroolefins, and carbon dioxide. The model showed good agreement with experimental data, as well as with predictions made by the extended corresponding state approach. In general, the absolute average deviation scored by the model was below 10% for all considered mixtures. However, a crossover term within the SAFT framework will be required to properly capture the enhancement in thermal conductivity near the critical point.