The quantum excitations of the collective magnetization dynamics in a
ferromagnet (F) - magnons - enable spin transport without an associated charge
current. This pure spin current can be transferred to electrons in an adjacent
non-magnetic conductor (N). We evaluate the finite temperature noise of the
magnon-mediated spin current injected into N by an adjacent F driven by a
coherent microwave field. We find that the dipolar interaction leads to
squeezing of the magnon modes giving them wavevector dependent non-integral
spin, which directly manifests itself in the shot noise. For temperatures
higher than the magnon gap, the thermal noise is dominated by large wavevector
magnons which exhibit negligible squeezing. The noise spectrum is white up to
the frequency corresponding to the maximum of the temperature or the magnon
gap. At larger frequencies, the noise is dominated by vacuum fluctuations. The
shot noise is found to be much larger than its thermal counterpart over a broad
temperature range, making the former easier to be measured experimentally
