Reticulated porous ceramic (RPC) made of ceria are promising structures used in solar thermochemical redox cycles for splitting CO₂ and H₂O. They feature dual-scale porosity with mm-size pores for effective radiative heat transfer during reduction and µm-size pores within its struts for enhanced kinetics during oxidation. In this work, the detailed 3D digital representation of the complex dual-scale RPC is obtained using synchrotron submicrometer tomography and X-ray microtomography. Total and open porosity, pore size distribution, mean pore diameter, and specific surface area are extracted from the computer tomography (CT) scans. The 3D digital geometry is then applied in direct pore level simulations (DPLS) of Fourier's law within the solid and the fluid phases for the accurate determination of the effective thermal conductivity at each porosity scale and combined, and for fluid-to-solid thermal conductivity from 10 to 1. Results are compared to predictions by analytical models for structures with a wide range of porosities 0.09-0.9 in both the strut's µm-scale and bulk's mm-scale. The morphological properties and effective thermal conductivity determined in this work serve as an input to volume-averaged models for the design and optimization of solar chemical reactors.