We measure the thermal conductivity of solid and molten tungsten using steady state temperature differential radiometry. We demonstrate that the thermal conductivity can be well described by application of Wiedemann-Franz law to electrical resistivity data, thus suggesting the validity of Wiedemann-Franz law to capture the electronic thermal conductivity of metals in their molten phase. We further support this conclusion using ab initio molecular dynamics simulations with a machine-learned potential. Our results show that at these high temperatures, the vibrational contribution to thermal conductivity is negligible compared to the electronic component.