Thermal conductivity of a highly porous carbon/carbon composite, known as carbon bonded carbon fiber (CBCF) and used as thermal insulation, was measured and related to the structure investigated by optical microscopy, x-ray diffraction and Raman spectroscopy. It was found that halogen purification of CBCF, that involves heat treatment in chlorine atmosphere, did not result in a greater extent of structural development than heat treatment at the same temperature for the same time in inert atmosphere (unpurified sample). The thermal conductivity of CBCF, both halogen purified and unpurified, was found to increase with temperature in the measured range 1000 degrees C to 2200 degrees C. The experimental thermal conductivity values were in good agreement with those calculated from a model that indicated that in CBCF solid heat transfer was dominant, compared to radiation heat transfer, even at 2200 degrees C. The matrix in CBCF was found to be relatively graphitic as a result of stress orientation on carbonization and as matrix was observed along the fiber length it was tentatively suggested that it may contribute to the effective axial conductivity of the fibers.