Data on thermal conductivity in states with hot electrons are necessary for the calculation of ultrashort laser exposure and the behavior of matter near the tracks of fast particles penetrating the condensed phase. We present a new analytical expressions describing the state of gold with the extra-high heat conductivity within a broad range of two-temperature phase diagram including the melting curve. This is a region in the three-dimensional space defined by the electron temperature, ion temperature and the density, in which the thermal conductivity is one order of magnitude larger than the value related to the room temperature. The growth of heat transfer is due to a sharp increase in the heat capacity of carriers (electrons) when they are heated and, accordingly, the gradual loss of the degeneracy. The developed model is based on a solution of the kinetic equation, involving experimental data and calculations of the electronic spectrum by the density functional method. The model works well also at low electron temperatures that allows to describe the crystallization of the melt as it cools down.