In this work, a method based on the Dual Reciprocity Boundary Element along with Sequential Function Specification scheme is suggested for solving two-dimensional inverse heat conduction problems involving unknown time and space varying boundary heat flux estimation. The measured transient temperature data utilized in the solution may be from locations inside the body or from locations on its inactive boundaries. The spatial variation of the unknown heat flux is approximated using polynomials, which is shown to conveniently reduce the number of unknowns in the inverse algorithm. The effectiveness and the reliability of the method are verified via a set of test data obtained by simulated experiments, which take into consideration various boundary heat flux characteristics. (C) 2003 Elsevier Ltd. All rights reserved.