A good astronomical site must fulfill several criteria including low atmospheric turbulence and low wind speeds. It is therefore important to have a detailed knowledge of the temperature and wind conditions of a location considered for future astronomical research. Antarctica has unique atmospheric conditions that have already been exploited at the South Pole station. Dome C, a site located on a local maximum of the Antarctic plateau, is likely to have even better conditions. In this paper we present the analysis of two decades of wind speed measurements taken at Dome C by an automated weather station (AWS). We also present temperature and wind speed profiles taken over four Antarctic summers using balloon-borne weather sondes. We will show that as well as having one of the lowest average wind speed ever recorded at an existing or potential observatory, Dome C also has an extremely stable upper atmosphere and a very low inversion layer.