  Motivated by recent discovery of strongly spin-orbit coupled two-dimensional
(2D) electron gas near the surface of Rashba semiconductors BiTeX (X=Cl, Br,
I), we calculate thermoelectric responses of spin polarization in 2D Rashba
model using an exact solution of the linearized Boltzmann equation for elastic
scattering. When the Fermi energy $E_{F}$ lies below the band crossing point we
find a non-Edelstein electric-field induced spin polarization which is linear
in $E_{F}$. We show that the Mott-like relation between spin polarizations
induced by the temperature gradient and electric field breaks down
significantly when $E_{F}$ lies in the vicinity of the band crossing point. As
the temperature tends to zero, the temperature-gradient induced spin
polarization vanishes. These results differ from previous ones obtained by
relaxation time approximations.
