In this study an adaptive observer is applied to an analysis of a distributed parameter system. The system considered is an unsteadily and uniformly heated circular cylinder, whose heat transfer coefficient is unknown. A set of equations for the lumped parameter system is obtained using the first four terms of eigenfunction expansion of the temperature field. The radial temperature distribution in the cylinder and the Biot number on its surface are estimated in a computer simulation using the input data of heating rate variation and the output data of temperature variation on the axis of the cylinder. The results reveal that the adaptive observer is useful for analysis of a certain type of heat conduction problems.