The thermal conductivity of gases depends strongly on the vibrational and rotational degrees of freedom of the molecule under consideration. Entropy scaling is based on the residual entropy, which does not capture the intramolecular and rotational contributions. This study proposes a model for the thermal conductivity that accounts for these degrees of freedom. We use the Chapman-Cowling approximation, where contributions of internal degrees of freedom to the thermal conductivity of an ideal gas are related to the self-diffusion coefficient. A resulting expression for the thermal conductivity is used as a reference in entropy scaling. We find experimental values for thermal conductivities in the entire fluid range to be (to good approximation) a function of residual entropy only. This study shows that entropy scaling is a strong approximation also for thermal conductivity, provided a suitable expression is chosen for the reference thermal conductivity.