In this paper, the iterative algorithm proposed by V.A. Kozlov and V.G. Maz'ya [Leningrad Math. J. 5(1990) 1207- 1228] is numerically implemented using the boundary element method (BEM) in order to solve the backward heat conduction problem (BHCP). The convergence and the stability of the numerical method are investigated and a stopping criterion is proposed. The numerical results obtained confirm that the iterative BEM product s a convergent and stable numerical solution with respect to increasing the: number of boundary elements and decreasing the amount of noise added into the input data.