We combine spin polarised density functional theory and thermodynamic mean
field theory to describe the phase transitions of antiperovskite manganese
nitrides. We find that the inclusion of the localized spin contribution to the
entropy, evaluated through mean field theory, lowers the transition
temperatures. Furthermore, we show that the electronic entropy leads to first
order phase transitions in agreement with experiments whereas the localized
spin contribution adds second order character to the transition. We compare our
predictions to available experimental data to assess the validity of the
assumptions underpinning our multilevel modelling.