= Solution
At room <temperature>, <electrons> require <quantum mechanics>, including their occupied orbitals or bands and <Fermi statistics>. Heavy nuclei can often be treated as distinguishable particles near classical equilibrium lattice sites, because their exchange wavelengths are short. Their coupled displacements form <phonons>, however, and the occupation of a vibrational mode is classical only if $k_BT\gg\hbar\omega$ for that mode. Even at room <temperature> some high-frequency modes remain quantum mechanical.
At $1$ K, quantum lattice vibrations, <zero-point motion> and the scarcity of thermally excited <phonons> are essential. Many heavy nuclei still do not have overlapping exchange <wavefunctions>; quantum vibration and quantum exchange are distinct criteria. For the same spacing, the nuclear overlap threshold from the rough estimate is $T_N\simeq211/A$ K, illustrating why the nuclear <mass> cannot be omitted from a blanket low-temperature claim.
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