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In this paper.we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems goveed by the parabolic partial differential equations.Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state.the boundary state and the final state.It is proven that these estimators are reliable bounds of the finite element approximation errors,which can be used as the indicators of the mesh refinement in adaptive finite element methods.