From the behavior of steel under thermal loads to the response of organic tissue to various stimuli, engineering research strives to develop constitutive models that allow us to understand and predict the physical world around us. Characterizing and understanding the constitutive behavior of materials is a pursuit limited by the expense and time associated with conducting and interpreting laboratory experiments. The focus of this thesis is to extend the development of an innovative computational method that aims to help circumvent the need for extensive tests as a basis for obtaining accurate and precise material response models. Specifically, this research involves the Autoprogressive training of Neural Networks for the inverse estimation of heat transport material models. This methodology, the Self Adaptive Finite Element Analysis (SAFEA), combines a Neural Network based Constitutive Model (NNCM) with a nonlinear Finite Element Program in an algorithm which uses very basic conductivity measurements to produce a constitutive model of the material under study: Through manipulating a series of Neural Network embedded Finite Element Analyses, it is demonstrated that an accurate constitutive model for a highly nonlinear material can be evolved and retained as an object to be used in the analysis of any problem involving the material under study. This thesis details the theoretical development of the SAFEA algorithm and provides a simulation of the SAFEA program through a steady-state non-linear heat transfer problem. The SAFEA program, coded in MATLAB, is included in appendix.