A transient heat transfer in the anisotropic space is investigated for the heat conductivity tensor’s components depending on the temperature. The analytical solution of the problem of pulse heating of the anisotropic space is used as groundwork. It is shown that the heat transfer waves exist in anisotropic spaces and have elliptic form with the properties depending on the ratio of the principal components of the heat conductivity tensor and on the nonlinearity of the anisotropic space. The analytical solution is constructed with the use of the sequence of self-simulated variables. The obtained result allows one to find out the temperature fields in the anisotropic bodies such as structural elements of flying vehicles subjected to the laser irradiation, the chemical heat sources effect, and the low-enthalpy gas flows effect.