Quite sure Sevan,

you by yourself state in your question  that x-rays 'bear' some energy. This energy is released to matter when that x-ray is absorbed by that matter, which is more or less the end of life of the x-ray.

1eV of x-ray energy is converted to 1,6x10-19J. So you can calculate the heat arising from each x-ray photon. Thus having a lot of x-rays (flux-rate) you have to add up all the energy contributions  of them.

Thus total heat production is proportional to x-ray energy and flux-rate.

The heat production profile in the matter is related to the flux decrease due to (energy dependent) attenuation of the x-rays.  

But taking the absolute numbers you will see that the heat production is very, very small; a signifucant increase in temperature is not really achieved.

Just some numbers:

Taking an x-ray tube (W-anode) at 100kVp and water sample at 1m distance:

you will have an increase of much less than 10-6°C/(mA*sec).

Having a rotating anode / CT tube (100mA) you will have much less than 10-4°C/sec increase in temperature.

Putting the sample at 10cm distance relative to this CT tube (100mA) will have an increase of much less than 10-2°C/sec

The term 'much less' is due to the fact that the limiting  numbers above are calculated under the assumption that the x-rays are stopped within the first cm of water, which for the high energetic photons is not the case at all. 

Well elaborated answer by Gerhard,

Heat, diffraction, photoelectron, etc. are some of the artifact phenomena in XRF process. Although heat release is not much tangible, for the instrument repeatability check, we used to run the samples alternately rather than one sample several times to avoid the heating of the fused beads