The well condition asymptotic waveform evaluation (WCAWE) is presented to solve heat conduction problem with different boundary conditions. The method introduced by R. D. Slone and his colleague to solve electromagnetic problems in the frequency domain. Specially, the novelty of this paper is: This is the first time WCAWE method is presented for thermal analysis, the method is presented for time-dependent problems. The general formulation procedure is given and various examples are solved to illustrate the capabilities of the proposed scheme. The results obtain in this work by using WCAWE method showed that, the WCAWE method successfully able to approximate the initial delay. Therefore, WCAWE method is able to remove the limitation of time domain AWE