We investigated superconductor/normal metal/superconductor (SNS) junctions made of short Au or Cu wires between Nb or Al banks. The Nb based junctions display inherent electron heating effects induced by the high thermal resistance of the NS boundaries. The Al based junctions show in addition subharmonic gap structures in the differential conductance d I/d V and a pronounced peak in the excess noise at very low voltages V. We suggest that the noise peak is caused by fluctuations of the supercurrent at the onset of Josephson coupling between the superconducting banks. At intermediate temperatures where the supercurrent is suppressed a noise contribution ∝1/ V remains, which reflects the strong nonequilibrium of quasiparticles even at very small voltages.