Proton-conducting electrolytes (PCEs) are extensively researched materials utilized in solid oxide electrochemical cells with various operating principles. The high ionic (protonic) transport of PCEs offers superior performance of such cells at reduced temperatures (400–600 °C). However, chemical-related deformations (strains) caused by the materials' hydration/dehydration pose serious technological challenges for fabricating multilayered (cer-cer, cer-met, and cer-glass) assemblies. Therefore, studying both thermal and chemical expansions of PCEs is crucial. This work presents in-depth high-temperature characterization of Sc-doped BaSnO₃ compounds (BaSn_1−xSc_xO_3−δ) in terms of their thermochemical expansion behavior. This characterization includes high-temperature X-ray diffraction and dilatometry analyses under various measuring conditions. On one hand, the collected data can serve as technological characteristics for the selection of appropriate functional materials. On the other hand, the thermochemical expansion data can be used to evaluate the thermodynamic parameters (enthalpy and entropy of hydration) and transport parameters (water chemical diffusion coefficient and chemical surface exchange constant) of PCEs. The latter was shown in the present work for the first time. This paves a new way to reveal the relationships between the composition, structure, thermochemical response, and transport properties of complex oxides capable of reversible water uptake.