Thermal conductivities of planetary materials under extreme conditions are important input parameters for modeling planetary dynamics such as accretion, geodynamo and magnetic field evolution, plate tectonics, volcanism-related processes etc. However, direct experimental measurements of thermal conductivity at extreme conditions remain challenging and controversial. Here we propose a new technique of thermal conductivity measurement in laser-heated diamond anvil cell (LH-DAC) based on radial temperature distribution around laser focal spot, mapped by imaging tandem acousto-optical tunable filter (TAOTF). The new technique provides much more information about heat fluxes in the laser-heated sample than existing static heating setups, and does not require dynamic numerical modeling using heat capacities in contrast to dynamic pulsed heating setups. In the test experiment, thermal conductivity of γ-Fe at conditions relevant to cores of terrestrial planets was measured.