We investigate the thermodynamics of first order non-ferromagnetic to ferromagnetic phase transformation in low thermal hysteresis alloys with compositions near Ni44Co6Mn40Sn10 as a basis for the study of multiferroic energy conversion. We develop a Gibbs free energy function based on magnetic and calorimetric measurements that accounts for the magnetic behavior and martensitic phase transformation. The model predicts temperature and field induced phase transformations in agreement with experiments. The model is used to analyze a newly discovered method for the direct conversion of heat to electricity [Srivastava et al., Adv. Energy Mater., 2011, 1, 97], which is suited for the small temperature difference regime, about 10-100 K. Using the model, we explore the efficiency of energy conversion thermodynamic cycles based on this method. We also explore the implications of these predictions for future alloy development. Finally, we relate our simple free energy to more sophisticated theories that account for magnetic domains, demagnetization effects, the crystallography of martensitic phase transformations and twinning.