  CP violation in the standard model originates from the
Cabibbo-Kobayashi-Maskawa mixing matrix. Upon integrating all fermions out of
the theory, its effects are captured by a series of effective nonrenormalizable
operators for the bosonic gauge and Higgs fields. We compute the CP-violating
part of the effective action to the leading nontrivial, sixth order in the
covariant gradient expansion as a function of temperature. In the limit of zero
temperature, our result addresses the discrepancy between two independent
calculations existing in the literature [1,2]. We find that CP violation in the
standard model is strongly suppressed at high temperature, but that at T<1GeV
it may be relevant for certain scenarios of baryogenesis. We also identify a
selected class of operators at the next, eighth order and discuss the
convergence of the covariant gradient expansion.
