We report the direct experimental observation of the temperature dependence of the persistent current Icj due to tunneling Cooper pairs along the c-axis intrinsic Josephson junctions integrated into YBa2Cu3O7−δ ring-shaped thin films. The measured Icj exhibits a linear temperature dependence over a wide range of temperatures well below Tc. Similar behavior was observed in different samples, confirming the reproducibility of the fabrication technique and the reliability of the results.