  We show the unique reconstruction of the heat-reflection coefficients in a
phonon transport equation. This is a mathematical model used to characterize
the dynamics of heat-conducting phonons in multiple layers of media, commonly
composed of metals and silicon. In experiments, the heat-reflection indices are
inferred by measuring the temperature at the surface of the exterior metal
after applying heat sources. In this article, we rigorously justify the unique
reconstruction of these indices by using such procedures.
