Sphalerons at Finite Temperature

We construct the sphaleron for several temperature-dependent effective potentials. We determine the sphaleron energy as a function of temperature and demonstrate that the sphaleron energy at a given temperature T is well approximated by the sphaleron energy at temperature zero scaled by the ratio of the vacuum expectation values of the Higgs field at temperatures T and zero. We address the cosmological upper bound on the Higgs mass.