= Solution
Degenerate <Electron>[electrons] conduct <heat> efficiently, making most of the interior nearly isothermal while an outer nondegenerate insulating envelope sustains a large <temperature gradient>. Nuclei have much larger masses and much smaller <Thermal de Broglie wavelength>[thermal de Broglie wavelengths] than <Electron>[electrons], so their <quantum degeneracy> is weak at these <Temperature>[temperatures]/densities, although <Coulomb coupling> and crystallization can matter. Under the stipulated classical ideal-carbon-ion approximation,
$$
\boxed{U=\frac32\frac{M}{12m_u}k_BT_c=\frac{Mk_BT_c}{8m_u}.}
$$
This excludes crystallization, <latent heat> and low-temperature heat-capacity changes; nondegenerate does not automatically mean weakly interacting.
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