Shape memory materials undergo temperature-induced martensitic phase transformations that involve reversible dimensional changes. In performing these changes in shape, the shape-memory material is able to do work against external constraints, and this is the basis for shape-memory low-temperature heat engines. The transformation temperatures on heating and cooling are often not very different (little hysteresis) and are well defined and reproducible. Furthermore, these temperatures can be adjusted by varying the composition of the shape memory alloy. Internal combustion engines dissipate approximately two-thirds of the fuel energy as heat to the exhaust and coolant systems. A low-temperature heat engine could convert a fraction of this heat energy to useful work. This paper discusses the conceptual basis for the application of shape memory heat engines to internal combustion engine powered vehicles. Metallurgical and thermodynamic factors are discussed, as well as engine efficiency.