The Finite Element Method (FEM) is used to improve the Extended Dynamic Plane Source (EDPS) method in order to obtain more accurate values of the thermal conductivity and diffusivity of the specimen. A method of the FEM-calculated response transformation into an analytical form that can be used in fitting the measured temperature response has been described and verified. Furthermore, a modification of the EDPS method designated as EDPS1 is designed, where only one piece of specimen is used. Since there is no analytical formula for the new method, the analytical formula for EDPS is used. The initial specimen parameter estimates for EDPS1 are accordingly very rough, and therefore the FEM numerical runs need to be repeated several times until the estimates reach relative errors of around 1%.