Indeed, the headline makes it sound like it is.

I want to hear what Sabine Hossenfelder says. I trust that she will say her honest truth.

Wouldn’t that be trivially the average velocity of the particles?

So, temperature is basically a measure of the average kinetic energy of particles in a substance. When you have an extremely diffuse gas, as is the case between galaxies, the particles can be moving very fast, but energy density is still low, because there are so few particles. According to the abstract of the paper, this gas is just 10^-3 particles/cm^3 or 1000 particles per cubic meter. That is 5 orders of magnitude less than the space between planets in our solar system.

So, yes, it is hot. But it also very, very sparse. According to Wikipidia 10^5 to 10^7 K[1]. But there isn't very much of it.

As to why they are hot, from what I've been able to find, it is at least partly due to gravitational potential energy being converted to thermal energy, as it falls into filaments.

[1]: https://en.wikipedia.org/wiki/Warm%E2%80%93hot_intergalactic...

Assuming it's not a fabrication of the press release, it may be jargon. Astrophysicists call "metal" everything that is not Hydrogen or Helium, but Chemist disagree heavily.

In this case, the paper don't call it "hot" but it says that 99.99% of the Hydrogen is ionized.

To ionize one Hydrogen you need 13.6eV. The average energy is temperature*k_Boltzmann. So if the temperature is 13.6eV/k_Boltzmann ~= 160000K then the 50% of the Hydrogen is ionized and 50% not ionized.

To get only 0.01% not ionized you need to increase the temperature, IIRC -log(0.01%)~=9 times.

So the temperature is ~1400000K. Unless I'm making an horrible stupid mistake, I agree it's hot.

(I may be missing the 4.7eV of the dissociation of H2 molecules into two H atoms, that would increase the temperature like a 40%.)