Experiments/papers about temperature dependence of persistent supercurrent?

Does someone know papers about direct experiments for the temperature dependence of persistent supercurrents in superconductors? This effect is unexplored, but it may explain a long-standing theoretical paradox. According to the BCS theory of superconductivity, the superfluid density smoothly decreases at warming. Hence, an eternal supercurrent must also smoothly decrease at temperature increase. However, all observations indicate that the running supercurrent is stable despite all temperature variations and abruptly disapears at a critical temperature. The theory/experiment paradox is open.