Why is the Warm-Hot Intergalactic Medium (WHIM) so hot, and what is "collisionless shock heating"? The Phys.org article Researchers find last of universe's missing ordinary matter says:

Ordinary matter, or &quot;baryons,&quot; make up all physical objects in existence, from stars to the cores of black holes. But until now, astrophysicists had only been able to locate about two-thirds of the matter that theorists predict was created by the Big Bang.
In the new research, an international team pinned down the missing third, finding it in the space between galaxies. That lost matter exists as filaments of oxygen gas at temperatures of around 1 million degrees Celsius, said CU Boulder's Michael Shull, a co-author of the study.

and refers to F. Nicastro et al, Observations of the missing baryons in the warm–hot intergalactic medium, Nature (2018). DOI: 10.1038/s41586-018-0204-1
The Wikipedia page Warm–hot intergalactic medium says:

Part of the gravitational energy supplied by these effects is converted into thermal emissions of the matter by collisionless shock heating

but the link to &quot;collisionless&quot; is ambiguous and I haven't a clue how a shock wave can get hot without collisions.
Is there a way to understand why is the Warm-Hot Intergalactic Medium (WHIM) is so hot, and what the &quot;collisionless shock heating&quot; process is that appears to be heating it?
Are the temperatures associated with the motion of the atoms and with the excited states of the atoms similar? With only of order 1 atom per cubic meter, collisions must be so infrequent that it seems to me that it might not be so hard for these two temperatures to diverge.
It should probably be added that the article includes a glaring error of the type you often see when the science writer apparently did not take an elementary astronomy class (this is why we have such classes!).  When the article states that the "lost matter exists as filaments of oxygen gas", you can be sure that Michael Shull never said any such thing, because that language clearly asserts that the "lost" matter is oxygen.  Of course what is meant is that the previously undetected baryons exist primarily as free protons (and electrons), which is merely evidenced by the presence of detectable oxygen that is simply assumed to be in the normal ratio we find between oxygen and hydrogen.  We could also quibble that calling it "lost" is hyperbole, a bit like saying the brain matter of the writer was heretofore "lost" because it couldn't be seen by looking into his/her ears, and was only recently "found" in some recent MRI.   Astronomers have long expected the WHIM to be there, and knew it would be hard to see, so it was hardly "lost."  But it is certainly nice to have greater certainty that it is there.

And not only is there a crucial assumption of the oxygen-to-hydrogen ratio, the OP is astute to ask how well we can even know the oxygen content itself.  All we see is the light from the oxygen, so we have to model how emissive it is to know how much oxygen is there.  That's not always easy at low densities where the emissivity can differ from what you'd get in local thermodynamic equilibrium, as was pointed out in the question and the first answer also.  So not all the uncertainties have been resolved, but it's certainly a nice step forward.

One final point regards why the gas is so hot.  This is related to the fact that low density gas cools itself very inefficiently, because cooling generally requires collisions between the particles (which generates the light).  Heating, on the other hand, can occur in various ways that might involve interactions with something other than the particles, say with cosmic rays or with magnetic fields.  Those latter elements can be present even if the density is very low, leading to high temperatures.  There is also a radiative cooling instability above about 10,000 K, where gas that is heated above that starts to cool less efficiently (as hydrogen gets all ionized), and responds by being compressed by the ambient pressure, which drives the temperature up even more.