Comment by thayne

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...