> Isn't "heating" a function of regular energy and matter?
I'm a bit confused at what made you think this. If there is any way to transfer energy from it to something else (which there must be, else it would be impossible to ever interact with it), then it can heat in exactly the same way as anything else.
> If it could heat up, Dark Matter wouldn't be dark.
I don't think this is correct at all. A system doesn't have to interact with EM to be thermodynamic. If you can define a temperature for it and there is the possibility for energy transfer, then it can heat up
I think this is where the debate is. I’m not a physicist but my understanding of the current dark matter models is that it doesn’t interact with itself in a way that could be thought of as “energy transfer” (ie. like particles that collide), but only gravitationally. This would mean there’s no real way for a dark matter “particle” to transfer momentum to another particle, and thus no real way for “heat” to exist as such.
Conceivably there could be interactions which are sufficiently constrained to prevent the equipartition theorem from coming into play in practice. For example, an interaction with a massive carrier may not be able to support thermal transfer except at very high energies.
Gravitational heat transfer would, I assume, work for everything, but it would also be very very slow.
We're a little bit spoiled by EM - it makes thermal interactions happen quickly and at all energy scales.
I think the confusing thing for me is that dark matter doesn’t interact with the electromagnetic field so it doesn’t reflect, absorb, or emit electromagnetic radiation.
That seems wrong. "Dark matter" usually means matter that doesn't interact with photons, not just "matter that is dark because no light is shining on it". But if it emits photons, even in a matter-antimatter reaction, then it couples with photons, and so it can't be dark matter in that sense.
Apparently (eg. [1]) there would be a couple of different pathways available for WIMP annihilation, to a W⁺W⁻ boson pair, or to μ⁺μ⁻ muon pair, or a e⁺e⁻ electron-positron pair, so the immediate annihilation products would be charged non-dark matter particles which would either quickly decay or annihilate into photons or simply shed their energy via normal EM interactions.
I'm a bit confused at what made you think this. If there is any way to transfer energy from it to something else (which there must be, else it would be impossible to ever interact with it), then it can heat in exactly the same way as anything else.