Many natural and man-made materials have the properties of varying thermal conductivity with directions. In the present work, the very short-time temperature response characteristics are examined by using a hyperbolic heat conduction model in an orthotropic medium when an axially symmetric heat flux with a temporal profile, which is either continuous or activated for period Delta t, is applied. The ratio of the thermal conductivities is one of the important parameters to be considered. The non-Fourier temperature responses in the orthotropic medium are compared with those in the isotropic case. The Fourier's results are also included and compared with the non-Fowrier's results.