We study the decay of the metastable symmetric phase in the standard m
odel at finite temperature. For the SU(2)-Higgs model the two wave fun
ction correction terms Z(phi)phi2, T) and Z(chi)(phi2, T) of Higgs and
Goldstone boson fields are calculated to one-loop order. We find that
the derivative expansion of the effective action is reliable for Higg
s masses smaller than the W-boson mass. We propose a new procedure to
evaluate the decay rate by first integrating out the vector field and
the components of the scalar fields with non-zero Matsubara frequencie
s. The static part of the scalar field is treated in the saddle point
approximation. As a by-product we obtain a formula for the decay rate
of a homogeneous unstable state. The course of the cosmological electr
oweak phase transition is evaluated numerically for different Higgs bo
son masses and non-vanishing magnetic mass of the gauge boson. For Hig
gs masses above approximately 60 GeV the latent heat can reheat the sy
stem to the critical temperature, which qualitatively changes the natu
re of the transition.