The unprecedented success of information technology has been focused by semiconductor industry to advance at dramatic rate. Thermal issues are hastily becoming one of the most challenging problems in high-performance chip design due to ever-increasing device. In the analysis of heat transport of IC chip, Fourier's heat conduction mechanism was frequently used. It is known that, this equation suggests a presumption of infinite thermal propagation speed. Then non-Fourier heat conduction model was used to forecast the rapid transient heat conduction process. A number of traditional iterative and moments matching based solvers can be found to analyze the Fourier and non-Fourier heat conduction model such as Runge-Kutta (RK) and Asymptotic Waveform Evaluation (AWE) technique. The iteration based RK method is computationally expensive and the AWE moment matching is inherently ill-conditioned.  In present work, Tiknonov based Well-conditioned Asymptotic Waveform Evaluation (TWCAWE) technique has proposed to analyze the Fourier and non-Fourier heat conductions. The TWCAWE technique is successfully able to avoid the ill-conditioning moment matching and also 1.2 times faster compared to AWE.