This work introduces the concept of thermal yield profile for the hot-spot identification with considering process variations and provides an efficient estimating technique for the thermal yield profile. After executing a mixed-mesh strategy for generating statistical polynomial expression of the on-chip temperature distribution, the thermal yield profile is obtained by a skew-normal based moment matching technique. Comparing with the Monte Carlo method, experimental results demonstrate that our method can efficiently and accurately estimate the thermal yield profile. With the same level of accuracy, our skew-normal based method achieves 215x speedup over the state of the art, APEX , for estimating the thermal yield profile. Moreover, results show that our mixed-mesh statistical polynomial expression generator achieves 130x speedup over the statistical collocation based method  and still accurately estimates the thermal yield profile.