In this paper, a linear electric machine is designed for the application of a free-piston engine to generate electrical energy. Due to the high thermal load on the mover, only machine topologies with a passive mover are considered. It is shown that flux-switching machines (FSM) are capable of fulfilling the requirements. A preceding thermal analysis provides the temperature distribution within the machine. The selection of the magnetic materials is determined based on the results. Subsequently an electromagnetic model for a 12 slot/14 pole FSM is created and optimized. Due to the application, the use of three design targets is appropriate: The efficiency $\eta$, the mass of the mover $m_{\mathrm{M}}$ and the permanent magnet (PM) mass $m_{\text{PM}}$. To take all the objectives into account, a multicriterial optimization using the NSGA-II algorithm is performed.