Given this cooling the temperature remains uniform. If the universe did expand forever it is my understanding that the cosmic radiation would continue to fill it to the outer reaches but continually cool down as the universe expands more slowly. This is already found to be the case. An excellent spectrum graph of the Cosmic Background can be found on the link below. In order to answer this question, I think it is important to first understand where radio sources come from.
Radio waves pour in from two regions called radio lobes on either side of the galaxy's dust lanes.
Centaurus A is in very close proximity to the Earth at only 13 million ly away. By the 1970's astronomers had discovered dozens of objects similar to Centaurus A which are called double radio sources. Cygnus A would be an example of an active galaxy usually found between two radio lobes. At radio wavelengths double radio sources are among the brightest radio sources in the universe. The idea that radio sources involve jets of particles traveling near the speed of light is supported by the existence of head tail sources.