We performed simultaneous measurements of the thermopower, and conductance of Au atomic contacts during the self-breaking process under temperature control. During the whole measurement temperature regime (290-330 K), the thermopower randomly fluctuated from positive to negative in sign, and the average thermopower was negligibly small with respect to the variation of the thermopower of the contact. Meanwhile, the standard deviation of the thermoelectric voltage increased linearly with the temperature difference across the contacts. Above 320 K, we observed a decrease in the standard deviation of thermopower, which suggested a decrease in the density of defects near the contacts. The linear increase in the standard deviation of the thermoelectric voltage, and the decrease in the standard deviation of the thermopower above 320 K, indicate that the standard deviation of thermopower provides insight into the thermopower of an individual Au atomic contact and the atomic structure of Au atomic contacts, such as crystallinity and the distribution of defects near the contacts.