Seismic observations suggest that the Earth’s inner core has a complex structure (e.g., the isotropic layer at the top, innermost inner core, and hemispherical dichotomy). These characteristics are believed to reflect the history of dynamics and temperature profile of the inner core. One critical physical property is the inner core’s thermal conductivity. The thermal conductivity of metals can be estimated from their electrical resistivity using the Wiedemann-Franz law. Recent high-pressure and temperature experiments revealed that the temperature dependence of electrical resistivity is small for Fe-Si alloys. The small temperature coefficient means that it is essential to determine the impurity resistivity of Fe alloys to constrain the inner core’s thermal conductivity. Therefore, this study systematically calculated the impurity resistivities of 4- and 6-component alloys at inner core pressure by combining the Korringa-Kohn-Rostoker method with the coherent potential approximation. As a result, we obtained the thermal conductivity of the inner core to be 150-263 W/m/K. The inner core cannot maintain thermal convection with such a high thermal conductivity, resulting in a flat temperature profile. In materials science, it is widely known that polycrystals soften suddenly at high temperatures a few percent below their melting temperature. If such a pre-melting occurs in the inner core, the flat temperature profile due to high thermal conductivity causes variations in the attenuation within the inner core. This may explain the observation that the upper inner core is more strongly attenuated than the innermost inner core.