We present an experimental study of the diffusive transport in a normal metal near a superconducting interface, showing for the first time the re-entrance of the metallic conductance at very low temperature. This new mesoscopic regime comes in when the thermal coherence length of the electron pairs exceeds the sample size. This re-entrance is suppressed by a bias voltage given by the Thouless energy and can be strongly enhanced by an Aharonov Bohm flux. Experimental results are qualitatively described by the linearized quasiclassical theory.