Abstarct: The thesis deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various meshfree approximations, and two improved meshless methods. The traditional two-point difference method is selected for the time discretization scheme. Two selected numerical examples are presented in this thesis to demonstrate the availability and accuracy of the present approach comparing with the traditional meshfree methods and finite element method. In the first chapter, we introduce the transient heat conduction problem, meshless methods and the needed definitions and theorems. The second chapter, express the finite element method and using of them for solving transient heat conduction problem. The third chapter consist of the traditional meshfree methods. In the forth chapter we introduce the improved meshless methods for solving the transient heat conduction problem and in the fifth chapter we show the numerical results. In this thesis all examples are solved by Matlab software.