We study the phase transition behavior of the ferroelectric BaTi0.8Zr0.2O3 in the paraelectric region. The temperature dependencies of thermal, polar, elastic, and dielectric properties indicate the presence of local structures above the paraelectric–ferroelectric transition temperature Tc = 292 K. The non-zero remnant polarization is measured up to a characteristic temperature T* ∼ 350 K, which coincides with the temperature where the dielectric constant deviates from the Curie–Weiss law. Resonant piezoelectric spectroscopy shows that DC field cooling above Tc using fields smaller than the coercive field leads to an elastic response and remnant piezoelectricity below T*, which likely corresponds to the coherence temperature associated with polar nanostructures in ferroelectrics. The observed remnant effect is attributed to the reorientation of polar nanostructures above Tc.