The abundance of large clusters of nucleons in neutron-rich matter at subnuclear density is found to be greatly reduced by finite-temperature effects when matter is close to β equilibrium, compared to the case where the electron fraction is fixed at Ye>0.1, as often considered in the literature. Large nuclei and exotic nonspherical nuclear configurations called pasta, favored in the vicinity of the transition to uniform matter at T=0, dissolve at a relatively low temperature Tu as protons leak out of nuclei and pasta. For matter at β equilibrium with a negligible neutrino chemical potential we find that Tuβ≃4±1 MeV for realistic equations of state. This is lower than the maximum temperature Tmaxβ≃9±1 MeV at which nuclei can coexist with a gas of nucleons and can be explained by a change in the nature of the transition to uniform matter called retrograde condensation. An important new finding is that coherent neutrino scattering from nuclei and pasta makes a modest contribution to the opacity under the conditions encountered in supernovas and neutron star mergers. This is because large nuclear clusters dissolve at most relevant temperatures, and at lower temperatures, when clusters are present, Coulomb correlations between them suppress coherent neutrino scattering off individual clusters. Implications for neutrino signals from galactic supernovas are briefly discussed.