Thermal properties such as specific heat C_p, thermal diffusivity a, and thermal conductivity \lambda of carbon fibers are important parameters in the behaviour of the carbon/carbon composites. In this study, the specific heat and the thermal diffusivity are measured at very high temperatures (up to 2500 K). The experimental thermal conductivity estimated by the indirect relation \lambda = a\rhoC_p is presented as a function of the temperature. Validations are carried out on isotropic metallic (tungsten) and ceramic (Al_2O_3) fibers. Measurements were obtained on three carbon fibers (rayon-based, PAN-based and pitch-based). Thermal conductivity results allow us to classify fibers from the most insulated to most conductive. The main result is that insulated carbon fibers have an increasing thermal conductivity when the temperature and the heat treatment temperature rise. Relationships between thermal conductivity and the structural properties (L_c and d_{002}) of such carbon fibers are studied. We also describe the influence of heat treatment on the thermal conductivity of carbon fibers.