We investigated the melting properties of a synthetic chondritic primitive mantle up to core–mantle boundary (CMB) pressures, using laser-heated diamond anvil cell. Melting criteria are essentially based on the use of X-rays provided by synchrotron radiation. We report a solidus melting curve lower than previously determined using optical methods. The liquidus curve is found between 300 and 600 K higher than the solidus over the entire lower mantle. At CMB pressures (135 GPa), the chondritic mantle solidus and liquidus reach 4150 (± 150) K and 4725 (± 150) K, respectively. We discuss that the lower mantle is unlikely to melt in the D″-layer, except if the highest estimate of the temperature profile at the base of the mantle, which is associated with a very hot core, is confirmed. Therefore, recent suggestions of partial melting in the lowermost mantle based on seismic observations of ultra-low velocity zones indicate either (1) a outer core exceeding 4150 K at the CMB or (2) the presence of chemical heterogeneities with high concentration of fusible elements. Our observations of a high liquidus temperature as well as a large gap between solidus and liquidus temperatures have important implications for the properties of the magma ocean during accretion. Not only complete melting of the lower mantle would require excessively high temperatures, but also, below liquidus temperatures partial melting should take place over a much larger depth interval than previously thought. In addition, magma adiabats suggest very high surface temperatures in case of a magma ocean that would extend to more than 40 GPa, as suggested by siderophile metal–silicate partitioning data. Such high surface temperature regime, where thermal blanketing is inefficient, points out to a transient character of the magma ocean, with a very fast cooling rate.