A microscopic study of superconducting fluctuation effects is applied to the investigation of various tunneling currents through an M1-I-M2 junction in which the temperature is just above the transition temperature Tc of the metallic film M2, and is well below that of the metal M1. The main contribution to the current in the voltage region eV ≃T-Tc ≪Tc comes from the tunneling of Cooper pairs, existing temporarily in M2 due to fluctuation. It is found out that this current exhibits a qualitatively different behavior according to the condition whether the transmission of particles through a barrier is specular or diffuse. If it is assumed to be specular, the behavior of the current agrees qualitatively with Ferrell's and Scalapino's results obtained by semiphenomenological discussions for the flucuations.