The models of thermal conductivity in fibrous spatially reinforced medium were developed at overall anisotropy of components; the approach is based on equality between dissipation in equivalent material and the considered composite. The calculated values of effective coefficients of thermal conductivity for two cases (unidirectional and cross-loaded) composites were compared with experimental data. Agreement between calculated and experimental data is satisfactory. It was demonstrated that developed models give the upper and lower estimates for effective coefficients of thermal conductivity in fibrous compositions.