A single isotope ratio (delta D or delta O-18) of water is widely used as an air-temperature proxy in Antarctic ice core records. These isotope ratios, however, do not solely depend on air-temperature but also on the extent of distillation of heavy isotopes out of atmospheric water vapor from an oceanic moisture source to a precipitation site. The temperature changes at the oceanic moisture source (delta T-source) and at the precipitation site (delta T-site) can be retrieved by using deuterium-excess (d) data. A new d record from Dome Fuji, Antarctica spanning the past 360 000 yr is presented and compared with records from Vostok and EPICA Dome C ice cores. In previous studies, to retrieve delta T-source and delta T-site information, different linear regression equations were proposed using theoretical isotope distillation models. A major source of uncertainty lies in the coefficient of regression, beta(site) which is related to the sensitivity of d to delta T-site. We show that different ranges of temperature and selections of isotopic model outputs may increase the value of beta(site) by more than a factor of two. To explore the impacts of this coefficient on reconstructed temperatures, we apply for the first time the exact same methodology to the isotope records from the three Antarctica ice cores. We show that uncertainties in the beta(site) coefficient strongly affect (i) the glacial-interglacial magnitude of delta T-source; (ii) the imprint of obliquity in delta T-source and in the site-source temperature gradient. By contrast, we highlight the robustness of delta T-site reconstruction using water isotopes records.