At each volume phonons behave harmonically in quasi-harmonic approximation. In real systems, there is anharmonicity/coupling between vibrational modes. Anharmonicity increases with increasing temperature and quasi-harmonic approximation should become less valid. 'Intermediate temperature' is a subjective term. Debye temperature probably sets the relevant temperature scale, I guess.
At each volume phonons behave harmonically in quasi-harmonic approximation. In real systems, there is anharmonicity/coupling between vibrational modes. Anharmonicity increases with increasing temperature and quasi-harmonic approximation should become less valid. 'Intermediate temperature' is a subjective term. Debye temperature probably sets the relevant temperature scale, I guess.