Redshift Preserves a Thermal Spectrum

Redshift preserves a black body spectrum, simply lowering the temperature in proportion to the scale factor: Tnow = aemit Temit. For example, the CMB was created at 3000K, at a scale factor of a = 10-3, so today's CMB has spectrum T = 10-3 %#215; 3000 K = 3 K.

 

Figure: this website.