Proton‐conducting ceramic electrolytes offer great potential for the development of low‐ and intermediate‐temperature solid oxide electrochemical devices, e.g., fuel cells and electrolyzers. However, the electrolyte constitutes the main bottleneck in such devices, especially at reduced temperatures, determining their overall performance and efficiency. Herein, for the first time the low‐temperature transport properties of BaSn0.8Y0.2O3−δ as a representative of proton‐conducting materials are investigated. The attention is focussed on grain and grain boundary conductivity of this ceramic material over a wide range of experimental conditions, including temperatures of 400–550 °C, oxygen partial pressures of 10−22–0.21 atm, and water vapor partial pressures of 10−5‐0.03 atm. After analyzing BaSn0.8Y0.2O3−δ with electrochemical impedance spectroscopy under these experimental conditions, the distribution of relaxation times is leveraged to evaluate the resistance, capacitance, and frequency of each electrolytic process. The data show that the BSY ceramic, prepared with CuO as a sintering additive, is characterized by three distinct processes: one is due to grain response, and two others are understood to be related to the responses of the pure and CuO‐covered grain boundaries. Therefore, this work opens a new path for the analysis of ionic, including protonic, transport along grains and grain boundaries.