Nuclear power is a powerful technology that plays an important role in the fight against climate change, and research is continuously engaged in studies that could further improve its safety. After the Fukushima accident, Accident Tolerant Fuels research has lead to new candidates for nuclear materials, such as SiC-fiber-reinforced SiC (SiCf/SiC). This material shows adequate nuclear, mechanical and chemical properties, but the thermal properties need further investigation. This thesis aims to fully characterize the thermal conductivity of this material, with a three-fold approach based on tomographic investigations, FEM modelling of heat transfer and experimental testing with a new, fully contactless technique. With synchrotron tomography, the microstructure of SiCf/SiC has been reconstructed. The results show a low degree of porosity, around 4%, but a troublesome network of pores and fibers. By rendering the features in 3D, they can be recognized and explained as a result of the manufacturing process. The internal structure has been used as a basis to create FEM models of the material at different size scales. Three microscopic models have evidenced a reduction of the thermal conductivity, relative to that of the matrix, by ca. 20% for SiCf/SiC, with minor anisotropic behaviour. Large scale models exhibit a considerable increase in the anisotropy, with the radial thermal conductivity being ca. 9.5% of the axial. This indicates a strong insulating effect from the large pores in the material, which are included in the large scale model. The main experiment setup completes the characterization. It is based on steady-steate thermal conductivity measurements with laser heating and infrared spectroscopy for temperature reconstruction. This experiment has been used to reconstruct the radial and axial thermal conductivities based on the temperature profile measured on the sample under the internal heat load from the laser. Results show a very strong difference between the radial thermal conductivity, below 3.5 W/m/K, and the axial one, generally above 20 W/m/K. A steady-state axial heat flow experiment has also been used, and it mostly confirms these findings. The results highlight the role of radiative heat transfer inside the material, typical of porous insulators. Its remarkable axial conductivity derives from the orientation of the fibers, which is semi-parallel to the cylinder's axis. The methodology established in this work has proven effective in the reconstruction of the thermal properties of candidate materials for nuclear fuel. Overall, the results show that steady-state measurements return a lower thermal conductivity compared to the literature of dynamic measurements on SiCf/SiC. This ought to be considered in the future for the characterization of prospective nuclear materials. This work also highlights areas for improvement in the manufacturing of fiber-reinforced materials for nuclear applications, and it provides insight on the influence of the internal structure of composites on their thermal performance.