To broaden the application of inverse estimation, the purpose of this study is to estimate the unknown temperature boundary condition of the complex or irregular shape, like the high pressure gas tank. An inverse algorithm based on the sequential method and the concept of future time combined with the finite-element method is proposed to solve the two dimensional irregular shape heat conduction problems. Special features about the proposed method are that the stiffness matrix of the irregular shape can be solved from the finite-element method and used by the inverse algorithm. The estimated results are quite accurate with the consideration of future time in the different measured errors, the various sensor's number and the sensor location. These results show that the proposed method is an accurate, sturdy, and efficient method for solving several realistic applications. (C) 2010 Elsevier Ltd. All rights reserved.