Bayesian approach has been widely used in inverse heat conduction problem (IHCP). However, due to either computationally prohibitive or analytically unavailable, its likelihood function is always intractable. In this study, to circumvent the intractable likelihood function, an approximate Bayesian computation (ABC) is extended to IHCP. However, massive expensive forward simulations are needed. It might lead to prohibited computational cost. In order to improve the efficiency of the ABC-IHCP, two strategies are proposed in this study. At first, in order to improve the convergence rate of ABC and reduce the number of samples, a none-parametric population Monte Carlo (NPMC) is proposed to determine the decreasing tolerance value adaptively. Secondly, in order to save the expensive computational cost of heat conduction simulation, the fast computational techniques are utilized. Based on the characteristics of the linear and nonlinear heat transfer problems, two heat conduction solvers are developed, respectively. The linear solver is based on superposition principle. As for the nonlinear problem, the fast and accurate reanalysis solver is suggested. Finally, the accuracy and efficiency of the suggested methods are verified with two numerical examples. (C) 2019 Elsevier Ltd. All rights reserved.