The structure of the amorphous fraction and the tensile-compressive stresses in amorphous-crystalline radiation-damaged zircon ZrSiO:U,Th depending on radiation dose and temperature (8–350 K) are investigated according to Raman spectroscopy of Boson peak for the first time. The Boson peak at 60–70 cm−1 associated with localized phonon states in the amorphous fraction ((Formula presented.)) is recorded at low temperatures ((Formula presented.) K) for samples with (Formula presented.) and over the entire temperature range 8–350 K for (Formula presented.). The wider localized states distribution in the latter case is considered as a sign of the amorphous phase structure evolution with an increase in radiation dose. The estimates of an atomic correlation radius based on the Ioffe–Regel criterion are similar to those in glasses, (Formula presented.) nm. The monotonic increase in (Formula presented.) value during heating of zircon with (Formula presented.) is governed by thermal expansion of the percolating amorphous fraction. The nonmonotonic variations of the (Formula presented.) value in zircon with (Formula presented.) is determined by the stresses in the amorphous fraction due to the mismatch in thermal expansion coefficient (CTE) and elastic moduli of the amorphous and crystalline phases depending on temperature; a change in the sign of the crystalline fraction CTE at 30 K is assumed. The Boson peak disappearance at 100 K in zircon with (Formula presented.) during heating conforms to with the violation of the phonon localization as a consequence of amorphous fraction contraction and partial ordering. The data obtained are important for predicting the thermal and mechanical properties of heterogeneous radiation-damaged materials and nanocomposites.