  We calculate the finite temperature self-energy for neutrinos in the presence
of a constant magnetic field in a medium in the unbroken $SU(2) \otimes U(1)$
model. We obtain the exact dispersion relation for such neutrinos and find that
the thermal effective mass is modified by the magnetic field. We also find a
simple analytic expression for the dispersion relation and obtain the index of
refraction for large neutrino momentum.
