I was reading the black body radiation and there the total energy of the black body radiation is $E=\sigma T^4$ and so specific heat is $C_v = 4 \sigma T^3$ so it is proportional to $T^3$.
I read that specific heat actually depends on degree of freedom of the system and also depends on the number of ways in which flow of heat can occur. So is in this case degree of freedom $3$? And is that where the $3$ in $T^3$ comes from?