Based on the homogeneous accretion model of planets, thermal evolution of the growing earth has been studied. After the surface of the growing earth starts melting owing to the blanketing effect of the primordial atmosphere, gravitational differentiation between metallic and silicate materials takes place in its upper region: the differentiation would give rise to a large amount of gravitational energy release as well as layered structure inside the proto-earth. A part of released energy would be transported outward by convection. Considering the effects of gravitational fractionation and convection, we have pursued numerically the evolution of the growing earth. Our results show that gravitational differentiation can supply energy large enough to keep the whole silicate layer in the molten state and that half of the released energy is conveyed outward by convective heat transport. In the growing stage, the temperature distribution in the silicate layer always lies between liquidus and solidus temperatures except in an uppermost thin zone. The thermal structure obtained favors a notion of the primordial magma ocean and of chemical differentiation of mantle. The structure of the growing earth which is composed of the central protocore, the metallic layer, and the silicate layer (magma ocean) would become gravitationally unstable and overturn to form a metallic core. Energy released by this overturn would not affect the structure of the upper magma ocean too much. But undifferentiated primordial materials which come from the protocore would add to mantle materials through the overturn and this would help explain the isotopic mantle heterogeneity presently observed.