  The thermalization rate for long wavelength fluctuations in the Higgs field
is calculated from the imaginary part of the finite temperature effective
action in the unbroken phase of the Standard Model. We use improved propagators
including a resummation of hard thermal loops. The thermalization rate is
computed at one loop level, but an estimate of the two--loop contribution
appears to give an indication that they are comparable to the one--loop result
for small thermal higgs mass. We show also that the Higgs field fluctuations
are likely to thermalize very fast compared with the electroweak phase
transition time.
