The present paper is concerned with coated‐fiber composites in which the fibers possess cylindrical orthotropy and may have an arbitrary orientation distribution. A micromechanics model is developed which predicts the effective thermal conductivity and estimates the local fields of such composites which may be subjected to uniform heat fluxes on its boundary. The micromechanics model is based on the Mori–Tanaka mean‐field concept [T. Mori and K. Tanaka, Acta Metall.21, 571 (1973)] and provides explicit expressions for the effective conductivity of the considered composite aggregate which is highly complicated. The analysis shows that special care is needed in formulating an effective theory of composites with constituents possessing curvilinear anisotropy.