  We show that the inclusion of a recently found additional term of the spin
polarization vector at local equilibrium which is linear in the symmetrized
gradients of the velocity field, and the assumption of hadron production at
constant temperature restore the quantitative agreement between hydrodynamic
model predictions and local polarization measurements in relativistic heavy ion
collisions at $\sqrt s_{NN}= 200$ GeV. The longitudinal component of the spin
polarization vector turns out to be very sensitive to the temperature value,
with a good fit around 155 MeV. The implications of this finding are discussed.
