Hot stuff gives off all kinds of radiation, yes.

Suppose you've got a ball of really hot stuff, that's somehow confined in that space so it can be considered thermalized. Each particle banging into the next has an average collision energy in the ~MeV, say. Not only will the nuclei be ~fully stripped of electrons (making for some very intense points of electric field), but everything zipping around will give rise to pair production, whether from electron-electron, electron-photon, photon-photon, or electron-nucleus* interactions.
*AFAIK, nuclei aren't important to the process, but their intense electric field is, and the nucleus serves as reaction mass, which is where the momentum balances for the "new" particle(s) produced.
Because of these interactions, temperature is not just the average energy, but the average mass-energy, and the sum must include the fraction of antimatter present, as well as the kinetic energy. The heat capacity of such a plasma should be quite high indeed, because more energy leads to more probability of pair production, and more pair production leads to higher intensity gammas, as well as all the bremsstrahlung making good old x-rays (except they're gammas too, because of the energy scale).
I think. I don't know of pair production being relevant to very hot electron-degenerate matter (white dwarfs). They're only in the millions of K, though. They're also gravitationally bound. And, their density is hyperbolic with energy, collapsing into a denser form of matter (i.e., neutron stars) when the electrons become relativistic, so at the same point where pair production might become relevant, gravity is too strong to matter and it blips into something else.
In any case, the spectrum would be continuum, because of the Doppler shift (you wouldn't expect to see 511keV gammas, but a very broad peak smeared out by the average kinetic energy), excess collision energy, and bremsstrahlung. There might be some \$\textrm{K}\alpha\$ lines (or gaps, for that matter) due to heavy, nearly-bare nuclei having atomic transitions (relevant to the case with lead, perhaps).
Tim