We observe a maximum in the conductance of Aluminum / n-GaAs junctions at temperatures 20 mK lower than the superconducting transition temperature. This is the first observation of a non- monotonic behavior of the conductance near the superconducting transition in superconducting normal junctions. To accommodate this effect we calculate the full temperature dependence of the conductance of these structures, invoking quasiclassical Green’s functions in the diffusive limit. In addition to the well-known low temperature peak at temperatures on the order of the Thouless energy, we find a maximum near the critical temperature. This peak has the same origin as the subgap conductance observed in superconducting-normal junctions at low temperatures. Its calculated magnitude and position are in good agreement with our experimental observation.