Highly stable varistor (voltage‐limiting) property is observed for ceramics based on donor doped Ba1-xSrxTi1-yZryO3 (x≪0.35, y≪0.05), when the ambient temperature (Ta) is above the Curie point (Tc). If Ta≪Tc, the same ceramics showed stable current‐limiting behavior. The leakage current and the breakdown voltage as well as the nonlinearity coefficient (α=30–50) could be varied with the Tc‐shifting components, the grain boundary layer modifiers and the post‐sintering annealing. Analyses of the current‐voltage relations show that grain boundary layer conduction at Ta≪Tc corresponds to tunneling across asymmetric barriers formed under steady‐state joule heating. At Ta≳Tc, trap‐related conduction gives way to tunneling across symmetric barriers as the field strength increases.