  We consider a spin-orbit-coupled two-dimensional electron system under the
influence of a thermal gradient externally applied to two attached reservoirs.
We discuss the generated voltage bias (charge Seebeck effect), spin bias (spin
Seebeck effect) and magnetization-dependent thermopower (magneto-Seebeck
effect) in the ballistic regime of transport at linear response. We find that
the charge thermopower is an oscillating function of both the spin-orbit
strength and the quantum well width. We also observe that it is always negative
for normal leads. We carefully compare the exact results for the linear
response coefficients and a Sommerfeld approximation. When the contacts are
ferromagnetic, we calculate the spin-resolved Seebeck coefficient for parallel
and antiparallel magnetization configuration. Remarkably, the thermopower can
change its sign by tuning the Fermi energy. This effect disappears when the
Rashba coupling is absent. Additionally, we determine the magneto-Seebeck
ratio, which shows dramatic changes in the presence of a the Rashba potential.
