The energy associated with the accretion of the earth and the segregation of the core is more than sufficient to melt the entire earth. In order to understand the thermal evolution of the early earth it is necessary to study the relevant heat transfer mechanisms. In this paper we postulate the existence of a global magma ocean and carry out calculations of the heat flux through it in order to determine its depth. In the solid mantle heat is transferred by the upward migration of magma. This magma supplies the magma ocean. The increase in the mantle liquidus with depth (pressure) is the dominant effect influencing heat transfer through the magma ocean. We find that a magma ocean with a depth of the order of 20 km would have existed as the earth accreted. We conclude that the core segregated and an atmosphere was formed during accretion.