This study develops a non-iterative method for estimating the boundary condition of transient heat conduction problems on the furnace inner wall based on the precise integration boundary element method (PIBEM). Generally, the problem of inversing boundary condition needs the iteration direct process about many times. The computational cost is high especially for inversing the transient boundary condition. However, the present method can directly inverse the temperature and heat flux boundary conditions by the least-square error method without iteration. In addition, using the precise integration method and BEM can fully play the superiority of solving the time-domain problem and reducing the dimension of problem, respectively. Meanwhile, an expanding coefficient method is introduced to approximate the unknown boundary condition. Numerical results show that the steady and accurate results can be obtained by the approximation of quadratic polynomials. A number of examples validate that the present method has very high efficiency and precision by investigating the effect of many factors such as the measurement error, the position and number of measurement points. (C) 2018 Elsevier Ltd. All rights reserved.