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Based on the joint inversion of seismic and gravity data in combination with the Gibbs free energy minimization method for calculating phase equilibria in the framework of the Na₂O-TiO₂-CaO-FeO-MgO-Al₂O₃-SiO₂ system, the influence of the thermal state on the chemical composition models of the mantle and the sizes of the Fe-S core of the Moon has been studied. The boundary conditions used are seismic models from Apollo experiments, mass and moment of inertia from the GRAIL mission. As a result of solving the inverse problem, constraints on the chemical composition (concentration of rock-forming oxides) and the mineralogy of a three-layer mantle are obtained. It is shown that regardless of the temperature distribution, the FeO content of 11–14 wt.% and magnesian number MG# 80–83 are approximately the same in the upper, middle and lower mantle of the Moon, but differ sharply from that for the bulk composition of the silicate Earth (Bulk Silicate Earth = BSE, FeO ~8 wt% and MG# 89). On the contrary, estimates of the Al₂O₃ content in the mantle rather noticeably depend on the temperature distribution. For the considered scenarios of the thermal state with a difference in temperature of 100–200°C at different depths, Al₂O₃ concentrations increase from 1–5% in the upper and middle mantles to 4–7 wt.% in the lower mantle with garnet amounts up to 20 wt.%. For the “cold” models, the bulk abundance of aluminum oxide in the Moon
is Al₂O₃ ~1–1.2 × BSE, and for the “hot” models it can be in the range of 1.3–1.7 × BSE. Concentrations of SiO₂ to a lesser extent depend on the temperature distribution and constitute 50–55% in the upper and 45–50 wt.% in the lower mantle; orthopyroxene, rather than olivine, is the dominant mineral of the upper mantle. Based on the modeling of the density of Fe-S melts at high Р-Т parameters, the sizes of the lunar core are estimated. The Fe-S core radii with an average density of 7.1 g/cm³ and a sulfur content of 3.5–6 wt.% are in the range of 50–350 km with a most likely value of about 300 km and rather weakly depend on the thermal regime of the Moon. The simulation results suggest that a lunar mantle is stratified by chemical composition and indicate significant differences in the compositions of the Earth and its satellite.