The resonant ultrasound spectroscopy of a specimen of (alpha)-quartz single crystal was carried out up to 558 (degrees)C, just below the (alpha)--(beta) transition (T[inf 0]=573 (degrees)C), and all of the independent elastic constants were determined simultaneously by the rectangular parallelepiped resonance method. The results show that bulk moduli decrease largely toward T[inf 0], while the shear moduli show only slight decreases. The constant, C[inf 14], characteristic of trigonal crystals, decreases to just below T[inf 0], but it seems not to vanish, but to remain a finite value, even at T[inf 0]. It is noted that the isotropic aggregate of (alpha)-quartz is a curious and scarce material, in the sense that its bulk modulus is smaller than the shear modulus, and Poisson's ratio is very small or even negative at temperatures higher than 450 (degrees)C. The effect of piezoelectricity of (alpha)-quartz on the theoretical frequencies was investigated in order to know whether the ordinary nonpiezoelectric theory gives considerably inaccurate resonance frequencies. It was shown that the nonpiezoelectric theory gives a frequency lower than the frequency given by piezoelectric theory, but the difference is 0.5% at most.