Convert radiation density into temp in degrees kelvin

Question

in the 1948 paper by Alpher he gives a present radiation density in gm per cm cubed. how is that converted to a temp of 5 degree kelvin

Answer 1

By using the integrated energy density of a blackbody radiation field, which is $$u = \frac{\pi^2}{15}\frac{(k_BT)^4}{(\hbar c)^3}\ .$$

Divide this by $c^2$ to get the equivalent mass density.