New composite materials are being continually developed for various industrial applications. In particular, a commonly manufactured type of composite consists of short fibers dispersed in a solid matrix. Most of the works in the literature treat the short fibers as isotropic ellipsoids of revolution. However, experimental evidences confirm that the short fibers approach the circular cylindrical shape, and often display a cylindrically orthotropic behavior. Few numerical studies have focused on global behavior of such short-fiber composites. In this paper we use an approach based on variational calculus, homogenization theory and the finite element method to calculate new, benchmark results for the components of the effective thermal conductivity tensor of longitudinally-aligned short-fiber composites with cylindrically orthotropic fibers. The three-dimensional periodic cell microstructrure consists of a circular cylindrical fiber placed at the center of a cube and along one of its horizontal axes. We generate tetrahedral finite-element meshes in the cell, and employ isoparametric quadratic discretization and conjugate gradient iteration to solve the cell problem and to obtain the numerical results for the effective conductivities of interest. These results are analysed and compared to previously reported results.