The phase boundary between β-Si3N4 and γ-Si3N4 is investigated at high-pressure and high-temperature using first-principles lattice dynamics calculations within the quasi-harmonic approximation. We find a positive slope of the phase boundary. It turns out that the thermal expansion of the spinel-type γ-phase is larger than that of the phenacite-type β-phase. On the other side, pressure affects more the volume of β-Si3N4 than of γ-Si3N4, reflected in the higher bulk modulus of γ-Si3N4. The origin of the different temperature behavior of these phases, consequently, goes along with a larger volume dependence of the zero point energy in γ-Si3N4 in comparison to β-Si3N4.