The thermal radiation emitted by a body is proportional to T^n ,...

According to the Stefan-Boltzmann law, the total energy radiated per unit surface area per unit time by a perfectly black body is directly proportional to the fourth power of its absolute temperature.

$E = \sigma T^4$

For a non-black body, the energy radiated is given by $E = \epsilon \sigma T^4$, where $\epsilon$ is the emissivity of the body. Since $\epsilon$ generally varies with temperature, the energy radiated by a non-black body is not exactly proportional to $T^4$.

Thus, $n = 4$ exactly for a blackbody.