To determine the complex of thermophysical characteristics of orthotropic bodies by the method of nondestructive monitoring, the authors examine three samples in the form of orthotropic half-spaces over whose surfaces a heat source and a sensor for measuring temperature at a fixed distance for the heat source move with a constant velocity. Temperature ranges in which the thermophysical characteristics are temperature-independent are studied. Excess temperature is determined by a heat conduction equation. The solution for the inverse coefficient problem of heat conduction for the orthotropic samples, using an inverse Fourier-Laplace transformation, is proposed. Expressions based on this solution for determining the thermal diffusivity, the thermal conductivity, and the specific heat are derived. The method can be used to measure temperatures on lines in the bounding surfaces of the samples.