  We found a strong influence of the composition of the magnetic material on
the temperature dependence of the tunneling magneto-Seebeck effect in $MgO$
based tunnel junctions. We use \textit{ab initio} alloy theory to consider
different $Fe_xCo_{1-x}$ alloys for the ferromagnetic layer. Even a small
change of the composition leads to strong changes in the magnitude or even in
the sign of the tunneling magneto-Seebeck effect. This can explain differences
between recent experimental results. In addition, changing the barrier
thickness from six to ten monolayers of $MgO$ leads also to a non-trivial
change of the temperature dependence. Our results emphasize that the tunneling
magneto-Seebeck effect depends very crucially and is very sensitive to material
parameters and show that further experimental and theoretical investigations
are necessary.
