This paper describes a new method of solving of inverse coefficient thermal conductivity problems in anisotropic bodies directed on the identification of temperature dependences of thermal conductivity tensor components. This method includes the following: quadratic residue construction between testing and theoretical temperature values, minimized gradient descent implicit method, parametric identification method, construction and numerical solution of conjugate problems relating to anisotropic thermal conduction, regularizing functional development based on prior assumptions on smoothness of temperature functions of thermal conduction components of anisotropic bodies, permitting to increase the whole method stability. Basing on this method many results were found relating to the identification of thermal conduction tensor components depending on temperature in the form of practically arbitrary functions: monotonous functions, having minimum and maximum points, flex points, etc. (C) 2018 Elsevier Ltd. All rights reserved.