The paper employs a theoretical model to evaluate the thermal conductivity of composites under two thermal assumptions which allow to solve the heat conduction equation. The composite is made of a ceramic-silica matrix and a fiber reinforcement. Three different materials are investigated as reinforcement, i.e. asbestos, steel and copper. The theoretical effective thermal conductivity is calculated along the three directions for a non-consumed composite and during its consumption. Numerical solutions of heat conduction in the composite are carried out. The anisotropy degree of the composite is investigated for the composite during its consumption. The anisotropic efficiency of the composite is defined as ratio between the anisotropy degree of the composite and the potential anisotropy of the two materials, i.e. the ratio between the thermal conductivity of the fiber and the matrix. The theoretical model allows to evaluate, under the two thermal assumptions, the anisotropic efficiency of the composites which decreases with the increase of the potential anisotropy reaching a minimum, which is only dependent on the geometry of the composite. (C) 2014 Elsevier Ltd. All rights reserved.