Extended X-ray absorption fine structure (EXAFS) has been measured at both the K edges of gallium and arsenic in GaAs, from 14 to 300 K, to investigate the local vibrational and thermodynamic behaviour in terms of bond expansion, parallel, and perpendicular mean square relative displacements and third cumulant. The separate analysis of the two edges allows a self-consistent check of the results and suggests that a residual influence of Ga EXAFS at the As edge cannot be excluded. The relation between bond expansion, lattice expansion, and expansion due to anharmonicity of the effective potential is quantitatively clarified. The comparison with previous EXAFS results on other crystals with the diamond or zincblende structure shows that the values of a number of parameters determined from EXAFS are clearly correlated with the fractional ionicity and with the strength and temperature interval of the lattice negative expansion.