The lattice parameter change with respect to temperature (T) has been measured using high-temperature powder X-ray diffraction techniques for high-temperature flux-grown GaPO4 single crystals with the alpha-quartz structure. The lattice and the volume linear thermal expansion coefficients in the temperature range 303-1173 K were computed from the X-ray data. The percentage linear thermal expansions along the a and c axes at 1173 K are 1.5 and 0.51, respectively. The temperature dependence of the mass density p of flux-grown GaPO4 single crystals was evaluated using the volume thermal expansion coefficient alpha(v)(T) = 3.291 x 10(-5) - 2.786 x 10(-8) [T] + 4.598 x 10(-11)[T](2). Single-crystal high-resolution Brillouin spectroscopy measurements have been carried out at ambient pressure from 303 to 1123 K to determine the elastic constants C-IJ of high-temperature flux-grown GaPO4 material. The single-crystal elastic moduli were calculated using the sound velocities via the measured Brillouin frequency shifts Delta nu(B). These are, to our knowledge, the highest temperatures at which single-crystal elastic constants of alpha-GaPO4 have been measured. Most of the room-temperature elastic constant values measured on flux-grown GaPO4 material are higher than the ones found for hydrothermally grown GaPO4 single crystals. The fourth-order temperature coefficients of both the Brillouin frequency shifts T-nu B((n)) and the single-crystal elastic moduli T-CIJ((n)) were obtained. The first-order temperature coefficients of the C-IJ are in excellent agreement with previous reports on low-temperature hydrothermally grown alpha-GaPO4 single crystals, while small discrepancies in the higher-order temperature coefficients are observed. This is explained in terms of the OH content in the GaPO4 network, which is an important parameter in the crystal thermal behavior.