A heated body radiates energy with a maximum intensity around the...

According to the Stefan-Boltzmann law, the total energy radiated per unit area per unit time by a body is given by $E = \epsilon \sigma T^4$, where $\epsilon$ is the emissivity and $T$ is the absolute temperature.

When the absolute temperature is doubled ($T' = 2T$), the new total energy emitted is $E' = \epsilon \sigma (2T)^4 = 16 \epsilon \sigma T^4 = 16E$.

Thus, the total energy emitted increases by a factor of $16$.

According to Wien's displacement law, the wavelength corresponding to maximum spectral emissive power is inversely proportional to the absolute temperature, $\lambda_m \propto \dfrac{1}{T}$.

Since frequency $\nu = \dfrac{c}{\lambda}$, the frequency corresponding to maximum intensity is directly proportional to the absolute temperature, $\nu_m \propto T$.

When the temperature is doubled, the frequency of maximum intensity also doubles. Thus, the new frequency is $2\nu_0$.