The optical absorption spectra of single crystals of MgCl₂ containing Fe²⁺ and Co²⁺ have been measured and the temperature dependence of the bands has been studied. For the transitions giving rise to hot bands, the energy of the initial state has been deduced from the temperature dependence of the integrated absorption. For MgCl₂:Co²⁺, spectra in the region of 19000 cm^-1 are presented, and one hot band has been identified. The spectrum of MgCl₂:Fe²⁺ shows several hot bands in the region of 23600 cm^-1. The energies found for the initial states of all these transitions agree well with the ground-state splittings calculated using the nearest-neighbour exchange parameters appropriate to pure FeCl₂ and CoCl₂. The spectrum of MgCl₂:Fe²⁺+Co²⁺ has an additional hot band at 23558 cm^-1 which has a lower state at 3.6 cm^-1. A simple model of the Fe²⁺-Co²⁺ exchange using the geometric mean approximation predicts an energy for this state of 3.8 cm^-1, in good agreement with the experimental result.