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The postdeposition annealing of magnetic tunnel junctions has become standard practice in junction fabrication to improve barrier properties. We have performed tunneling measurements at elevated temperatures during the annealing process on plasma-oxidized, MgO barrier, magnetic tunnel junctions. The data were interpreted in terms of the Hartman model which accounts for an asymmetric barrier profile. The results could not be interpreted solely by the temperature smearing of the Fermi distribution and so the electrode/barrier/electrode structure had been altered during the annealing. While the barrier height at one interface improved, the other was degraded. Our experiments lead us to believe that this is due to the diffusion of Mn to the barrier/pinned electrode interface. We show that through transport and tunneling magnetoresistance measurements it is possible to monitor physical processes such as material migration during the annealing process.