In this work inverse estimations of the temperature dependent thermal conductivity of homogeneous 1D materials have been made (linear, sinusoidal, piece-wise and rectangular continuous dependencies) under forced convection, constant heat flux and adiabatic boundary conditions. The input data are the temperature history at only a particular location of the material (not necessary inside the solid). No prior information is used regarding the waveforms of the unknown thermal conductivity functions. A piece-wise function is used to approximate the solution by means of a programming routine that minimizes a classical predefined functional, where each stretch of this function was obtained step by step by increasing or decreasing its slope. The network simulation method is used to solve both the direct and inverse problems numerically. A comparison of the real and estimated thermal conductivity was made to confirm the validity of the proposed method.