The order-disorder transitions in Cu-Al-Mn shape-memory alloys have been studied experimentally by means of calorimetric techniques. Results are compared with Monte Carlo simulations of a simplified BlumeEmery-Griffiths model. A first order DO3 A2 transition is obtained for the stoichiometric Cu3Al alloy, while for concentrations near Cu2AlMn two second order transitions are found: L21 B2 and B2 A2. Despite the simplicity of the model, the agreement between experimental and simulation results is remarkably good. Finally, the metastable phase diagram of bcc Cu-Al-Mn alloys is presented.