This document presents a study estimating the boundary shape of a functionally graded material using an inverse method and finite element analysis. The study models heat transfer through the material using partial differential equations. An inverse algorithm based on the conjugate gradient method is used to estimate the unknown boundary shape based on temperature measurements. The boundary shape is allowed to change iteratively until the estimated temperature distribution matches measured values. The method is intended to estimate shapes that cannot be directly observed, such as boundaries exposed to high temperatures. The accuracy of the approach is demonstrated on test problems of varying complexity.