We predict an anomalous 0-蟺 transition in Josephson junctions with a ferromagnetic-insulator (FI) barrier. Previously it wasfoundthattheground stateofsuch junctions alternates between0and 蟺 states when the thickness of FI is increasing by a single atomic layer. By solving the Bogoliubov de-Gennes equation and using the Furusaki-Tsukada formula, we show that similar 0-蟺 transition canbe also inducedby increasing temperature T. Therefore the existence of 蟺 state can beexperimentally con铿乺medby simply observing the nonmonotonic T dependence of the Josephson critical current.