In this paper, the inverse Laplace transform via. fast Fourier technique was presented to solve the inverse heat conduction problem. It is known that the measurement error for the interior temperature always causes the numerical solution of the inverse heat conduction problem unstable.The authors solved this problem by the concept of the spectral analysis. A brief description of the correlation of the different locations in the solid body where the interior temperature was measured, the measurement error for the interior temperature and the time stept of the numerical method is also included. The results of calculation show the method presented here is quite valuable to the scientific research for transient phenomena.