Abstract: By using the equivalence between the solution of boundary problem for differential equation and functional extreme value, cut-and-try methods are used for the finite element methods (FEM) , solution of unstable temperature-field inside grain-layer in the process of grain drying. A process is introduced to transform functional heat transfer partial differential equation into FEM discreteness, solution of extreme value and forming FEM equation . It provides an effective channel for predicting variation of temperature-field inside grain-layer in the process of grain drying with time. Meanwhile, it is experimentally verified with the satisfactory results. Without man-made airflow, the major factors affecting prediction accuracy are the measurement of flow-in surface heat and the selection of heat conductivity value of grain. This study lays down the foundation for simulation of more complex cases.