This paper presents an improved space marching technique for estimating the transient thermal boundary conditions including heat flux and temperature, based on the measured interior temperature history. The algorithm employs a fully implicit difference scheme thus is unconditionally stable for various space and time steps. In each space marching step, the number of used future temperatures can be randomly designated. The proposed method was tested with numerical and experimental data to verify its performances for both linear and nonlinear problems. Comparisons between the proposed method and the method of Raynaud and Bransier (1986) were also conducted using both the numerical and experimental data. In the testing with numerical data, the present method is better than the method of Raynaud and Bransier (1986) for small time steps where the estimating accuracy was dominated by the random error. In the testing with cryogenic quenching experimental data, it was found that the present method is applicable for processing temperature data involving local fluctuations and abrupt changes. By incorporating more future temperatures in each space marching step, the present method demonstrated a better performance in processing the experimental data. (C) 2018 Elsevier Ltd. All rights reserved.