The stationary problem about the structure of temperature field in the \((m+1)\)-layered orthotropic wedge-like parachute space is considered. This problem is studied for boundary conditions of the first and the second type, which are formulated on a conic surface. By application of the method of fundamental functions and the Fourier transform, the exact analytical solution of the problem is constructed. The analysis of solutions with respect to the type of boundary conditions is fulfilled.