Not quite.. As we go back in time, the universe was SMALLER, DENSER and HOTTER. If we go back FAR enough, the universe was so crushingly small and hot that matter (protons and electrons) and radiation were coupled. At this early stage, the radiation could not freely move without being immediately absorbed by electrons.

When the Universe was about 300,000 years old, it had expanded and cooled enough that the thermal radiation could finally escape, a bit like how trapped radiation finally escapes from the surface of our Sun (only it stays INSIDE the universe!).

Radiation from our Sun has a Black-Body temperature equal to the surface of the Sun (5800 K degrees). Radiation at recombination has the Black-Body temperature of the Universe at this time, when it was 300,000 years old and 10,000 K degrees. HOWEVER, the Cosmic Background Radiation we see NOW is cold, 2.7 K degrees, because the universe has expanded, and the photons have been REDSHIFTED to very, very long wavelengths..