[en] The sequential function specification method proposed first by Beck is considered as one of the most efficient methods for the inverse heat conduction problem (IHCP) which is extremely ill-posed and time-dependent. This method determines an open-quotes inverse solutionclose quotes advancing in a sequential fashion in time. The values estimated at any given time depend on the solution obtained previously. The main question connected with this method is the stability; i.e., the cumulative error in the solution must remain bounded at all time. Since the first paper of Beck in 1970, few theoretical stability analyses have been studied in the literature. The aim of this paper is to find the conditions under which this method is stable irrespective of the data measurements. For a 1D linear IHCP, we try to construct a sequence such that the coefficients α are independent of the data measured and the convergence of the series summation ^∝_i=1|X_i| guarantees the stability of the method. In other words, we need to find an adequate condition on a α, such that summation ^∝_i=1|X_i is convergent, implying that the method is stable. The values of α, depend on the discretization size h of the function to be determined q(t) and the sliding time horizon (or future time interval) τ of the method. The range of values of h and τ which give the values of α, such that the series summation ^∝_i=1|X_i | is convergent is established numerically. Under the stability condition, an error estimation of the Beck's method is derived. The approach presented could be also applied to multidimensional IHCPs, in which the coefficients α_i, and X_i are no longer scalar but become square matrices