= Solution
Lattice vibrations contribute a <phonon> <heat capacity>. At temperatures well below the <Debye temperature>, its leading contribution is proportional to $T^3$, whereas the electronic part is proportional to $T$:
$$
\boxed{C_{V,m}\simeq\gamma T+\beta T^3}.
$$
The lattice term can therefore become important rapidly as <temperature> rises, even if the electronic term dominates sufficiently close to zero. At higher <temperature> the lattice contribution approaches the <Dulong-Petit law> value $3R$ per mole of atoms within the harmonic approximation. This is not a claim that the low-temperature $T^3$ law holds at all temperatures.
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