The problem of heat conduction in a two-dimensional orthotropic cylinder, subject to asymmetric and periodic temperature distributions on the outer wall, was solved analytically. The results depend on the non-dimensional frequency (alpha), outer to inner cylinder radius ratio (R(2)), Blot number (Bi), and orthotropicity factor (K-t). Insulation characteristics of orthotropic cylinders may be significantly better than those of isotropic cylinders.