Thermal conductivity as a function of temperature and density (top row) and as a function of density along the initial and final planet profile (bottom row). Top: total conductivity heat map as a function of density and temperature for the three different conductivity models (from left to right): Cond-1, Cond-2, and Cond-3. The color represents the total conductivity value. Black lines show an example temperature-density profile for a planet with M_p = 10 M_⊕ under the hot start scenario, calculated with the respective conductivity model: AESOPUS (Marigo et al. 2024; Eberlein & Helled 2025), FR17 (French & Redmer 2017), F19 (French 2019), and C07(Cassisi et al. 2007). The upper line (Initial profile) corresponds to the initial state of the evolution, while the lower line (Final profile) represents the state after 10 Gyr. The dotted line indicates a convective region within the planet. Hatched regions with diagonal lines (radiation dominated), squared lines (vibration dominated), and dots (electron dominated) indicate where a specific conductivity mechanism contributes more than 50% to the total conductivity. Colored lines with labels mark the boundaries of the conductivity models similarly to Figure 1. For this plot, we assumed Z = 0.20 for the radiative conductivity and Z = 1.0 for the electron conductivity of C07. We note that the distribution of heavy elements changes within the planetary interior. Bottom: conductivity as a function of density for the initial (gray) and final (black) profiles shown in the top panel. The thick solid line shows the total conductivity along the density–temperature profile of the planet, while the thin solid (radiative), dashed (vibrational), and dotted (electron) lines show the individual conductivity contributions.