A general scheme for calculating ternary recombination rate constants of atomic species based on a hybrid quantum–classical nonadiabatic dynamics approach is presented and applied to the specific case of the ternary recombination of atomic ions of argon in cold argon plasmas. Rate constants are reported for both fine-structure states of the ion, and , T = 300 K, and for selected values of the reduced electric field. A thorough comparison with the literature data available for T = 300 K and a couple of close temperatures is performed with a favorable agreement achieved. It is shown that the excited ions may contribute to the formation of dimer ions,, as efficiently as the ground-state ions, , due to fast internal conversion of the electronic energy, which takes place in ternary collision complexes, .