Why does the idea of dust blocking starlight from afar not resolve the Olbers Paradox?

According to the second law of thermodynamics, there can be no material hotter than its surroundings that does not give off radiation and at the same time be uniformly distributed through space. Energy must be conserved, per the first law of thermodynamics. Therefore, the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in intense uniform radiation as bright as the collective of stars themselves, which is not observed.