The geometry of a furnace inner wall is estimated by an inverse method in this work. Based upon the concept of a virtual area, in the analysis process the heat conduction equation with boundary conditions was first discretized by a finite difference method to form a matrix equation. And then the linear least-squares error method was applied to determine the temperature of virtual boundary by inverse process. Finally, the geometry of the furnace inner wall can be obtained by direct process. Furthermore, the effects of the measurement errors. number of measurements and position of measurements on the deviation of geometry prediction are also discussed. (c) 2007 Published by Elsevier Ltd.