From high-precision Brillouin spectroscopy measurements, six elastic constants (C11, C33, C44, C66, C12, and C14) of a flux-grown GeO2 single crystal with the α-quartz-like structure are obtained in the 298–1273 K temperature range. High-temperature powder X-ray diffraction data is collected to determine the temperature dependence of the lattice parameters and the volume thermal expansion coefficients. The temperature dependence of the mass density, ρ, is evaluated and used to estimate the thermal dependence of its refractive indices (ordinary and extraordinary), according to the Lorentz–Lorenz equation. The extraction of the ambient piezoelectric stress contribution, e11, from the C′11–C11 difference gives, for the piezoelectric strain coefficient d11, a value of 5.7(2) pC N−1, which is more than twice that of α-quartz. As the quartz structure of α-GeO2 remains stable until melting, piezoelectric activity is observed until 1273 K.