{bf Context.} Numerical models of the evolution of interstellar and integalactic plasmas often assume that the adiabatic parameter $gamma$ (the ratio of the specific heats) is constant (5/3 in monoatomic plasmas). However, $gamma$ is determined by the total internal energy of the plasma, which depends on the ionic and excitation state of the plasma. Hence, the adiabatic parameter may not be constant across the range of temperatures available in the interstellar medium. {bf Aims.} We aim to carry out detailed simulations of the thermal evolution of plasmas with Maxwell-Boltzmann and non-thermal ($kappa$ and $n$) electron distributions in order to determine the temperature variability of the total internal energy and of the adiabatic parameter. {bf Methods.} The plasma, composed of H, He, C, N, O, Ne, Mg, Si, S, and Fe atoms and ions, evolves under collisional ionization equilibrium conditions, from an initial temperature of $10^9$ K. The calculations include electron impact ionization, radiative and dielectronic recombinations and line excitation. The ionization structure was calculated (...) using the Gauss elimination method with scaled partial pivoting. Numerical integrations (...) were carried out using the double-exponential over a semi-finite interval method. In both methods a precision of $10^{-15}$ is adopted. {bf Results.} The total internal energy of the plasma is mainly dominated by the ionization energy for temperatures lower than $8times 10^4$ K with the excitation energy having a contribution of less than one percent. In thermal and non-thermal plasmas composed of H, He, and metals, the adiabatic parameter evolution is determined by the H and He ionizations leading to a profile in general having three transitions. However, for $kappa$ distributed plasmas these three transitions are not observed for $kappa<15$ (...). In general, $gamma$ varies from 1.01 to 5/3.
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