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The structural and dielectric characterization of 30% Sn-doped BaTiO3 (BaSn0.3Ti0.7O3) as a function of temperature is carried out combining, complementary probes to reveal structural modifications associated to the relaxor behavior. Dielectric data confirms the existence of relaxor-type behavior in BaSn0.3Ti0.7O3. The local and average structural changes as a function of temperature have been investigated in the region of broad changes of dielectric response. Local probes, such as x-ray absorption fine structure spectroscopy and Mössbauer spectroscopy reveal a special trend of the lattice related to the diffuse dielectric phase transition as observed from dielectric data. The analysis of Raman spectra as a function of temperature reveals a peculiar behavior in the temperature region corresponding to the dielectric transition. The analysis of x-ray diffraction patterns points out a pseudocubic structure throughout the temperature range while the volume exhibits a negative thermal expansion in the region of broad dielectric maximum. Our results suggest structural modifications occurring in the system throughout a wide temperature range, interestingly, associated with changes in macroscopic properties of relaxors such as dispersion in dielectric constants and raising of dipole moments.