Answer
If the plate is cooled, the peak of maximum radiated intensity shifts toward longer wavelengths.
Work Step by Step
We can write the equation for the peak wavelength at a given temperature $T$:
$\lambda = \frac{2.9\times 10^6~nm~K}{T}$
We can see that if $T$ decreases, then the peak wavelength $\lambda$ increases.
Therefore, if the plate is cooled, the peak of maximum radiated intensity shifts toward longer wavelengths.
