An identification problem is discussed for the boundary conditions of a deterministic distributed-parameter system governed by a partial differential equation of parabolic type. A method based on the fundamental ideas of the boundary element method is proposed for identification of unknown boundary conditions. The identification problem is formulated by using the ideas of boundary partition and weighted residual expression corresponding to the given partial differential equation. The boundary conditions are estimated by the method of least squares using the state observations taken at the interior points. A numerical example illustrates the applicability of the proposed method for boundary identification.