The early thermal evolution of Moon has been numerically simulated to understand the magnitude of the impact‐induced heating and the initially stored thermal energy of the accreting moonlets. The main objective of the present study was to understand the nature of processes leading to core–mantle differentiation and the production and cooling of the initial convective magma ocean. The accretion of Moon was commenced over a time scale of 100 yr after the giant impact event around 30–100 million years in the early solar system. We studied the dependence of the planetary processes on the impact scenarios, the initial average temperature of the accreting moonlets, and the size of the protomoon that accreted rapidly beyond the Roche limit within the initial 1 yr after the giant impact. The simulations indicate that the accreting moonlets should have a minimum initial averaged temperature around 1600 K. The impacts would provide additional thermal energy. The initial thermal state of the moonlets depends upon the environment prevailing within the Roche limit that experienced episodes of extensive vaporization and recondensation of silicates. The initial convective magma ocean of depth more than 1000 km is produced in the majority of simulations along with the global core–mantle differentiation in case the melt percolation of the molten metal through porous flow from bulk silicates was not the major mode of core–mantle differentiation. The possibility of shallow magma oceans cannot be ruled out in the presence of the porous flow. Our simulations indicate the core–mantle differentiation within the initial 102 to 103 yr of the Moon accretion. The majority of the convective magma ocean cooled down for crystallization within the initial 103 to 104 yr.

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