  We have developed a tunneling theory to describe the temperature dependence
of tunneling magnetoresistance (TMR) of the magnetic tunnel junctions (MTJs)
with periodic grating barrier. Through the Patterson function approach, the
theory can handle easily the influence of the lattice distortion of the barrier
on the tunneling process of the electrons. The lattice distortion of the
barrier is sensible to the temperature and can be quite easily weakened by the
thermal relaxation of the strain, and thus the tunneling process of the
electrons gets changed highly with the variation of the temperature of the
system. That is just the physical mechanism for the temperature dependence of
the TMR. From it, we find that the decrease of TMR with rising temperature is
mostly carried by a change in the antiparallel resistance ($R_{AP}$), and the
parallel resistance ($R_{P}$) changes so little that it seems roughly constant,
if compared to the $R_{AP}$, and that, for the annealed MTJ, the $R_{AP}$ is
significantly more sensitive to the strain than the $R_{P}$, and for
non-annealed MTJ, both the $R_{P}$ and $R_{AP}$ are not sensitive to the
strain. They are both in agreement with the experiments of the MgO-based MTJs.
Other relevant properties are also discussed.
