  The 3-dimensional gauge-Higgs system describes the non-perturbative infrared
effects of the high-temperature phase of the Standard Model. We calculate the
two-loop self-energies in the 3-dimensional SU(2) Higgs model and in the
corresponding gauged non-linear $\sigma$-model. As an application of the
results, we estimate the dynamically generated vector boson mass in the
symmetric phase of the Higgs model by means of gap equations.
