Do higher frequency/energy levels in the EM spectrum mean higher temperatures? I am trying to find concrete evidence that for example, light in the optical spectrum would be hotter than infrared light because it has a higher frequency, and that is directly proportional to energy. Is energy directly proportional to temperature?
If we are to split up the optical spectrum into its components, blue light has a higher frequency than red light, and blue light is hotter than red light. Does this work for the whole spectrum?
 A: Light of a specific wavelength does not have a well-defined "temperature" - however, it does have energy.
The Planck law tells us that the spectrum of a black body of a certain temperature covers a range of wavelengths, and the Wien displacement law tells us what the peak of that distribution is as a function of temperature.
The actual radiation from a warm body will be the black body radiation modified by the emissivity of the surface - so in principle, a hot surface that has very little emissivity at short wavelengths might appear "redder" than a cooler surface that has low emissivity in the longer wavelengths - but in practice that would be quite hard to achieve.
Cooler objects have essential their entire emission in the (near)-infrared band, but the same rules still apply: the cooler the object, the longer the emitted wavelengths. The microwave background of the universe corresponds to a temperature of about 2.7 K - and it follows the same laws of physics.
A: It's complicated. If we are talking about temperature of an object then yes. The hotter the object is the higher the electromagnetic wavelength frequency it generates. From infrared to UV going from 200 degrees to 4000 celcius. In terms of radiation absorption. On a black object then the hottest frequency is about yellow. Not red or infrared as most common objects don't absorb it.
A: Molecules of matter at given temperature have satisfy below relation,
$\Delta E=NkT\tag1$
where $N$ is number of particles, in this case number of molecules and $T$ is temperature.
From planck's law, energy difference of higher frequency level is given by,
$\Delta E=Nhf\tag2$
where $N$ is number of particles, here it is number of photons and $f$ is frequency of photon.
From (1) & (2),
$f=\dfrac{k}{h}T=bT\tag3$
where $k$ is boltzmann's constant, $h$ is planck's constant and $b$ is equivalent to wein's constant and called as wein's constant in frequency in terms of two constants.
From (3), frequency is directly related to temperature this is wein's law if ratio of $f$ and $T$ is equal to $b$. Then that frequency, $f_m$ is frequency at which intensity of radiation is maximum and it is different for different temperatures.
This is theoretical calculation, if one find it's not true then it's anomaly of theory.
