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There is much controversy concerning thermoelectric effects in the MgO-based magnetic tunnel junctions (MTJs) as reported in some recent publications. To clarify the problem, we give calculations from atomic first-principles systemically. Large Seebeck coefficient ( S ) and up-limit of figure of merit (ZT) are predicted in double- and multi-barrier MTJs, with those in single-barrier MTJs being relatively small. By restraining the phonon thermal conductance through the introduction of one vacuum barrier or numbers of MgO barriers, the up-limit of ZT can be obtained. Room temperature $S\approx -220\quad \mu {\rm{V}}{{\rm{K}}}^{-1}$ and ZT $\approx \;3.5$ are predicted in an asymmetric Fe $| $ MgO $| $ Fe $| $ Vaccum $| $ Fe MTJs. The resonant quantum-well states are suggested to be responsible for the enhanced thermoelectric effects in the MTJs with double- and multi-barrier.