An inverse analysis is used to estimate linearly temperature dependent thermal conductivity components k(x)(T), k(y)(T) and specific heat capacity C(T) per unit volume for an orthotropic solid. Simulated measured transient temperature data are generated by adding random errors to the exact temperatures computed from the solution of the two-dimensional, direct transient heat conduction problem. An iterative procedure, based on minimizing a sum of squares function with the Levenberg-Marquardt iterative procedure is used to solve the inverse problem.