Carbon fiber-reinforced carbon (C/C) composites consist in a carbon matrix holding carbon or graphite fibers together, whose physical properties are determined not only by those of their individual components, but also by the layer buildup and the material preparation and processing. The complex structure of C/C composites along with the fiber orientation provide an effective means for tailoring their mechanical, electrical, and thermal properties. In this work, we use the Laser Flash Technique to measure the thermal diffusivity and thermal conductivity of C/C composites made up of laminates of weaved bundles of carbon fibers, forming a regular and repeated orthogonal pattern, embedded in a graphite matrix. Our experimental data show that: i) the cross-plane thermal conductivity remains practically constant around (5.3 ± 0.4) W·m−1 K−1, within the temperature range from 370 K to 1700 K. ii) The thermal diffusivity and thermal conductivity along the cross-plane direction to the fibers axis is about five times smaller than the corresponding ones in the laminates plane. iii) The measured cross-plane thermal conductivity is well described by a theoretical model that considers both the conductive and radiative thermal contributions of the effective thermal conductivity.