  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 is 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 timescale of 100 years 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 one
year 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 re-condensation 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 $10^2$-$10^3$ years of the Moon accretion. The majority of
the convective magma ocean cooled down for crystallization within the initial
$10^3$-$10^4$ years.
