The invention concerns a composite material comprising activated carbon and expanded graphite. The material is a block wherein the activated carbon is homogeneously and uniformly distributed in the form of microporous particles. The texture of said particles is characterised by a microporous volume W0 ranging between 0.1 cm3g−1 and 1.5 cm3g−1 and a mean pore dimension L0 ranging between 2 Å and 30 Å, the activated carbon particles have substantially the same texture wherever they are located in the composite material, the thermal conductivity levels of the material range between 1 and 100 Wm−1K−1. Said material is obtained by heat treatment of a mixture of expanded graphite and an activated carbon precursor in the presence of an activating agent at a temperature and for a time interval sufficient to obtain a wear rate of the activated carbon precursor ranging between 5 and 70% by mass.