The temperature and magnetic dependence of the Josephson supercurrent are measured in order to study the effects of the flux change in Josephson junctions. A study is made of the regime near the transition temperature where the junction is full of vortices and the variations of the flux are caused by the change of the London penetration depth. Detailed study of Jc versus T in constant fields indicated that an oscillatory Jc versus T behavior will occur as one varies the temperature of the junction.