The generation of the magnetic fields, the geodynamo, in the outer core works like a heat engine through heat transfer across the core-mantle boundary (CMB) and the freezing of the solid inner core. These thermal and chemical energy sources power the geodynamo which in turn also drives the mantle convections and plate tectonic movements. The heat transfer from the core into the mantle thus places key constraints on the dynamics and thermal evolution of deep Earth. However, recent studies on the thermal conductivity and heat flux across the CMB reach controversial conclusions at Earth’s core conditions. Here we measured the electrical resistivity of hcp-iron at the core conditions using a suitable four-probe van Der Pauw sample geometry and homogeneous flat-top laser heating in a diamond anvil cell (DAC) to the relevant pressure-temperature of the Earth’s core. The measurements were also combined with in situ X-ray diffraction at GSECARS, Advanced Photon Source to allow direct examinations of the crystal structure, equation of state, and possible textures. We found that the resistivity for hcp-iron sample increases quasi-linearly with increasing temperatures at the relevant pressure of the core, which could be fitted by the Bloch-Grüneisen formula. Our experimental results agree with the theoretical model that consider both electron-phonon and electron-electron contributions to the conductive property in hcp-Fe at high pressures and temperatures. By applying a non-ideal Lorenz number to convert the resistivity of hcp-iron to thermal conductivity at high pressure-temperature, we have reliably contrained the resistivity and thermal conductivity of hcp-iron at the topmost outer core P-T conditions. We have further considered the effects of melting and light element alloying on the transport properties of Fe to constrain the heat flow across the core-mantle boundary. These results are applied to constraint the thermal and composition energy sources for the geodynamo and the age of the inner core through Earth’s history.