  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 $\gamma$-ray emission dominated by the prompt de-excitation
nuclear lines and $\pi^0$-decay $\gamma$-rays. Using a large nuclear reaction
network, we compute the time evolution of the chemical composition of such hot
plasmas and their $\gamma$-ray line emissivity. At higher energies, we provide
simple but accurate analytical presentations for the $\pi^0$-meson production
rate and the corresponding $\pi^0\to2\gamma$ 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 $\gamma$-ray emissivity.
