On the shot-noise limit of a thermal current
  The noise power spectral density of a thermal current between two macroscopic dielectric bodies held at different temperatures and connected only at a quantum point contact is calculated. Assuming the thermal energy is carried only by phonons, we model the quantum point contact as a mechanical link, having a harmonic spring potential. In the weak coupling, or weak-link limit, we find the thermal current analog of the well-known electronic shot-noise expression. 
Kelly R. Patton