  We investigate diffusive nanowire-based structures with two normal terminals
on the sides and a central superconducting island in the middle, which is
either grounded or floating. Using a semiclassical calculation we demonstrate
that both device layouts permit a quantitative measurement of the
energy-dependent sub-gap thermal conductance $G_\mathrm{th}$ from the spectral
density of the current noise. In the floating case this goal is achieved
without the need to contact the superconductor provided the device is
asymmetric, that may be attractive from the experimental point of view. Our
calculations are directly applicable to the multi-mode case and can serve as a
starting point to understand the shot noise response in open one dimensional
Majorana device.
