High-precision measurements of the temperature dependence of the (111) extremal cross-section area of the neck of the Fermi surface of gold have been carried out by means of the de Haas-van Alphen effect in the temperature and field ranges 4<or approximately=T<or approximately=17K and 48<or approximately=H<or approximately=71.5 kG, respectively. The area is found to decrease approximately as the fourth power of the temperature with a coefficient which is over twice that expected from the effect of lattice expansion alone. The difference is attributed to the modification of the effective potential seen by the carriers due to thermally excited lattice vibrations. The observed area shifts corrected for constant volume provide an estimate of the electron-phonon interaction parameter for electronic states in the vicinity of the L(2') point in the Brillouin zone at the Fermi level.