On this link, it states the following: "large assemblies of galaxies that are permeated by even larger amounts of diffuse gas. With temperatures of 10 million degrees or more".
How are these diffused (ionized) gas able to become so hot when they are in large distances from one another and have very little density?
What that ESA (European Space Agency) page titled Hot gas sloshing in a galactic cauldron that you link to describes are called WHIM (Warm–Hot Intergalactic Medium). They are not interstellar medium, but intergalactic medium gas. The difference in density is huge, with interstellar medium density at an average of $\rho ∼ 1\ ppcm$ (one proton per cubic centimeter), but the density of these WHIM being even a few orders of magnitude lower at $\rho ∼ 10^{−6}−10^{−5}\ ppcm$, or roughly 1 to 10 protons per cubic meter (NASA's Chandra X-ray Observatory quotes average density of 6 protons per cubic meter).
What is interesting about WHIM is that they are absolutely huge. We're talking of distances that extend across clusters of galaxies (so stretching multiple millions of light years), which means that even as tenuous as they are, account for a large portion of the baryonic matter of the Universe:
Such matter is predicted to account for a sizable fraction ($∼ 50\%$) of all the baryons in the local ($z < 1$
[redshift in the infrared spectrum]) Universe, and it is thus considered the best candidate to host the baryons seen at high redshift and missing from the low redshift census.
So now about their heat emissions, and why are they detected in the X-ray range in the first place (the ESA's article mentions the photograph featured there was taken by the ESA’s XMM-Newton X-ray observatory):
Electrons and baryons in the WHIM are shock-heated during their infall in the dark matter LSS
[Large–Scale Structures]potential well, and settle in filamentary/sheet-like structures surrounding LSSs.
I've added a few clarifications in quotes encapsulated in square brackets, but what this means is that parts of these WHIM interact with AGN (Active Galactic Nucleus) as the galaxies pass by, and the X-ray emissions of AGN excite Baryonic matter to a temperature $T ∼ 10^5−10^7 K$.
Quote sources:
Additional reading:
Just to add to TidalWave's answer - something that is easier to simply imagine, the trivial "why".
What we call Temperature on thermodynamic level is Speed on atomic level. Saying the medium has a high temperature is equivalent to saying particles of that medium move awfully fast.
Well, they must be moving fast. They must be moving faster than the escape speed of the galaxies, or the ones ejected from galaxies wouldn't escape them and the primordial would get captured by the galaxies instead. Being so sparse they collide extremely rarely too - so whatever slowdowns resulting from collisions (expending energy e.g. as photons) simply almost never happens. In short, you're getting particles that were fast (hot) enough to get (and remain) there at all, and had no opportunity to cool down.
They are hot in the sense of particle speed, but if you were out there, you will get freezed, since there is such a low density that any of these particles will likely impact you (and transfer you its energy, which is what you would notice as heat) while you will cold due to radiation.
