  Thermal effects in the broken phase of the electroweak theory are studied in
the strongly interacting Higgs boson limit. In that limit and at tree level the
bosonic sector of the theory is a gauged non-linear sigma model. The associated
one-loop thermal effective action for soft fields is then computed by using the
background field method together with the Stueckelberg formalism. This
effective action describes thermal corrections to the masses of the gauge
bosons W, Z and the photon. It is the proper generalization of the hard thermal
effective action of a Yang-Mills theory when there is a Higgs mechanism for a
heavy Higgs particle.
