X-Rays have no temperature, they are EM radiation, not matter.
I weep for whoever told you a collection of photons can't have a temperature in the same way a collection of particles can. Who was it? Was it... no one?
Black body radiation has a characteristic temperature just like the black body that produced it, however in the case of the photon gas [wikipedia.org] it's the Plank's Law distribution of energy in photons rather than the Maxwell?"Boltzmann distribution which describes the matter.
If there's any sloppiness in the title at all it's specifying just the X-rays when you'd technically have to include all photon energies to get the correct temperature, just like you would include all the particles in a gas or solid. However I think it's pretty much in the noise [wolframalpha.com] as far as inaccuracy goes. Unlike your statement. Sorry.
P.S. Such radiation has a temperature and *also entropy*, which is inversely proportional to temperature. So for example if you assume the earth is more or less in equilibrium with the sun, that means the total energy received is equal to the total energy output, but the temperature of the received radiation is much higher, meaning less energy, meaning the earth is emitting a net-positive amount of entropy. In case you've ever wondered how exactly the whole "the earth is not a closed system; it's powered by the sun" thing worked in terms of entropy.
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