The history of using first order phase transformations to convert heat into other forms of energy stretches back as far as the 1600's, when the first steam engine was invented. This method can be further applied to any first order phase transformation beyond the liquid-vapor systems. Multiferroic materials undergoing phase transformations, during which a ferroic property changes drastically, are promising candidates, especially in the small temperature difference regime. In this thesis I investigate the conversion from heat into electricity by this new method. A family of alloys undergoing martensitic phase transformation with a big change of magnetization is demonstrated to be capable of energy conversion. It is shown by construction of a demonstration that the proposed concept is feasible. Also the idea of using a temperature gradient for this new energy conversion method is examined. The analysis shows that it is possible to convert a temperature gradient to a temperature oscillation by automatically moving the specimen in two conservative force fields: gravity and magnetic field. Quasi-static and finite-time thermodynamic models are developed. Based on the models, the efficiency and power output of this new method is evaluated theoretically, and the directions of design improvement are proposed. The Clausius-Clapeyron relation (the effect of magnetic field on the transformation temperature) is found to be a key thermodynamic relation in this method. The utilization of other types of muliferroic phase-transforming materials is surveyed.