Effective grain core or single crystal dielectric constants of four solid oxide electrolytes-yttria-stabilized zirconia (YSZ with 8 and 7 mol% yttria), tetragonal zirconia polycrystals (TZP with 3 mol% yttria), strontium- and magnesium-doped lanthanum gallate (LSGM), and gadolinia-doped ceria (GDC, with 20 mol% gadolinia)-were studied as a function of temperature by AC-impedance spectroscopy and equivalent circuit fitting. Unlike their undoped counterparts, the acceptor-doped oxides consistently exhibited an upturn in effective grain core/single crystal dielectric constant in the vicinity of 350-500 K. This temperature-dependent behavior was attributed to the onset of thermally activated dipolar relaxation-an explanation supported by the appearance of loss tangent peaks at higher temperatures. Differences between "effective" dielectric constants and frequency-dependent complex dielectric constants for the grain core/single crystal frequency range, and applications of the effective dielectric constant data are discussed.