The presented thesis focuses on study of transport and thermoelastic properties of materials under conditions of planetary interiors by means of high-pressure experimental tools and finite element modeling, and their role in the dynamics and states of cores of terrestrial planets. Experiments in laser-heated diamond anvil cell (LHDAC) in combination with numerical simulations of heat transfer in DAC are shown to yield information on thermal conductivity of a pressurized sample. The novel technique consists of one-sided laser heating and double-sided temperature measurements and utilizes a precise determination of several parameters in course of the experiment, including the sample geometry, laser beam power distribution, and optical properties of employed materials. The pressure-temperature conditions at the probed portion of the sample are, however, not uniform. To address this problem, thermal pressure in the laser-heated diamond anvil cell and anisotropic thermal conductivity originating from the texture development upon uniaxial compression have been studied by means of numerical simulations. The method for determination of thermal conductivity is applied to iron at pressures up to 70 GPa and temperatures of 2000 K, meeting the Earth’s lower mantle conditions and covering Mercury’s entire core. The obtained results are extrapolated to the conditions of the Earth’s core-mantle boundary using a theoretical model of the density dependence of thermal conductivity of metals and published values on Grüneisen parameter and bulk modulus. After considering the effect of minor core elements, the obtained value at these conditions supports case for the downward revision of the thermal conductivity in the core. From the point of view of core dynamics and energy budget, the lower thermal conductivity implies more favorable conditions to drive the dynamo. Similar scenario applies for Mercury where, for high values of thermal conductivity, heat flux conducted along the iron-core adiabat exceeds the actual heat flux through the core-mantle boundary. This leads to a negative rate of entropy production in the core that makes it impossible to sustain the dynamo process presumably responsible for the observed magnetic field of Mercury.