A self-consistent model of thorium dioxide and its dilute alloys with cerium is developed. Thermal and elastic properties of ThO2 and several variations of Ce[Formula: see text]Th[Formula: see text]O2 synthesized by various techniques (powder processing and pelletization (POP) and coated agglomerate pelletization process (CAP) and using two different atmospheres, i.e., air or Ar[Formula: see text]H2 mixture) are simulated. The influence of porosity on degree of phonon anharmonicity and on the lattice properties (in particular, thermal conductivity) of the considered systems is analyzed.