The disclosure relates to a system and method for recovering waste heat to improve the response and fuel economy of a machine. The system includes a heat recovery apparatus and an engine. The heat recovery apparatus has a cold cylinder, a first piston disposed in the cold cylinder, a hot cylinder, a second piston disposed in the hot cylinder, and a regenerator. The first piston and the second piston are in fluid communication with one another via the regenerator. The engine produces heat from multiple sources. A first heat source produced by the engine is thermally coupled to the regenerator and a second heat source produced by the engine is thermally coupled to the hot cylinder. The heat recovery apparatus is configured to convert the heat generated by the first and second heat sources into mechanical energy.