The thermal radiation emitted by a body is proportional to Tⁿ where T is its absolute temperature. The value of n is exactly 4 for

As per Stefan's law, emissive power of a body is given by

$\mathrm{E}={\mathrm{\sigma \epsilon AT}}^4$, where T is its absolute temperature.

This is true for any body. $\epsilon$ is emissivity of the body. Its value varies from 0 to 1. It is 1 for black body.