The mass shift, width broadening, and spectral density for ρ and ω mesons in a heat bath of nucleons and pions are calculated using a general formula which relates the self-energy to the real and imaginary parts of the forward scattering amplitude. We use experimental data to saturate the scattering amplitude at low energies with resonances and include a background Pomeron term, while at high energies a Regge parametrization is used. The real part obtained directly is compared with the result of a dispersion integral over the imaginary part. The peaks of the spectral densities are little shifted from their vacuum positions, but the widths are considerably increased due to collisional broadening. Where possible we compare with the UrQMD model and find quite good agreement. At normal nuclear matter density and a temperature of 150 MeV the spectral density of the ρ meson has a width of 345 MeV, while that for the ω is in the range 90-150 MeV.