The process of thermolysis of barium hydroxostannate BaSn(OH)6 as a precursor for preparing barium stannate BaSnO3 has been investigated using the method of differential thermal analysis. Thermal decomposition products of the precursor were characterized using X-ray diffraction, IR spectroscopy, low-temperature nitrogen adsorption, and scanning electron microscopy. It was shown that dehydration at nearly 270 °C resulted in the formation of an X-ray amorphous multiphase product, from which single-phase barium stannate crystallized at temperatures above 600 °C. The synthesized barium stannate was used as a functional additive to prepare composite proton electrolytes in the CsHSO4-BaSnO3 system. The structural and transport properties of the obtained system were investigated. It is shown that the highly conductive state of the salt is stabilized in a wide range of temperatures. High conductivity values of composite solid electrolytes in the medium temperature range create the possibility of their use as solid electrolyte membrane materials.