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We present current noise measurements in a long diffusive
superconductor-normal-metal-superconductor junction in the low voltage regime,
in which transport can be partially described in terms of coherent multiple
Andreev reflections. We show that, when decreasing voltage, the current noise
exhibits a strong divergence together with a broad peak. We ascribe this peak
to the mixing between the ac- Josephson current and the noise of the junction
itself. We show that the junction noise corresponds to the thermal noise of a
nonlinear resistor 4kBT=R with R V = I V and no adjustable parameters.
