Very hot plasmas with ion temperature exceeding $10^{10}$ K can be formed in certain astrophysical environments. The distinct radiation signature of such plasmas is the $γ$-ray emission dominated by the prompt de-excitation nuclear lines and $π^0$-decay $γ$-rays. Using a large nuclear reaction network, we compute the time evolution of the chemical composition of such hot plasmas and their $γ$-ray line emissivity. At higher energies, we provide simple but accurate analytical presentations for the $π^0$-meson production rate and the corresponding $π^0\to2γ$ emissivity derived for the Maxwellian distribution of protons. We discuss the impact of the possible deviation of the high energy tail of the particle distribution function from the "nominal" Maxwellian distribution on the plasma $γ$-ray emissivity.

11 pages, 10 figures