The conductivity σ, quantum-based magnetoconductivity Δσ = σ(B) - σ(0), and Hall coefficient RH (= µH/σ) of degenerate, homoepitaxial, (010) Si-doped β-Ga2O3, have been measured over a temperature range T = 9-320 K and magnetic field range B = 0-10 kG. With ten atoms in the unit cell, the normal-mode phonon structure of β-Ga2O3 is very complex, with optical-phonon energies ranging from kTpo ~ 20-100 meV. For heavily doped samples, the phonon spectrum is further modified by doping disorder. We explore the possibility of developing a single function Tpo(T) that can be incorporated into both quantum and classical scattering theory such that Δσ vs B, Δσ vs T, and µH vs T are all well fitted. Surprisingly, a relatively simple function, Tpo(T) = 1.6 × 103{1 - exp[-(T + 1)/170]} K, works well for β-Ga2O3 without any additional fitting parameters. In contrast, Δσ vs T in degenerate ScN, which has only one optical phonon branch, is well fitted with a constant Tpo = 550 K. These results indicate that quantum conductivity enables an understanding of classical conductivity in disordered, multi-phonon semiconductors.