  We estimate the thermoelectric response, namely, the Seebeck coefficient of a
hot and deconfined plasma of quarks and gluons, created post ultrarelativistic
heavy ion collisions in the presence of a weak, homogeneous background magnetic
field. We employ the kinetic theory framework, wherein we use the relativistic
Boltzmann transport equation in the relaxation time approximation. In-medium
interactions are taken into account via the quasiparticle masses of the partons
extracted from one loop perturbative thermal QCD. We calculate the individual
Seebeck coefficients of the quark species from which we show that the Seebeck
coefficient of the medium can be obtained as a weighted average. Both the
individual and total Seebeck coefficients are seen to decrease with temperature
and increase with the chemical potential. We find that a larger current quark
mass has an amplifying effect on the individual Seebeck coefficient in the
presence of a weak magnetic field. We also draw comparisons of Seebeck
coefficients between the cases of weak and strong background magnetic field. We
observe that the temperature sensitivities of the individual Seebeck
coefficients increase with the current mass of the quark species in the case of
a weak magnetic field whereas the same records a decreasing trend for strong
magnetic field. The total Seebeck coefficient in weak magnetic field has a
feeble positive magnitude and variation with temperature, quite different from
the behaviour of the individual coefficients. This is a consequence of the
weighted average prescription that we use to calculate the total Seebeck
coefficient from the individual ones. For the composite medium, the magnitude
and sign of the Seebeck coefficient and its variation with temperature, for the
weak $B$ case is found to be significantly different from the strong $B$ case.
