This paper reports on the design of the thermal energy conversion system for the Prometheus-L inertial fusion energy power plant, emphasizing features affected by characteristics of the fusion thermal power source. Ebasco Services is part of a team led by McDonnell Douglas, and funded by the Department of Energy, developing power plant designs for both laser and heavy-ion drivers with the goals of advancing the state of Inertial Fusion Energy design, identifying critical issues, and providing a basis of comparison with Magnetic Fusion Energy design studies. The thermal cycle design is based on an advanced supercritical double reheat Rankine cycle which utilizes as its heat sources the liquid lead coolant from the first wall protection, the helium coolant for the blanket and waste heat from the laser-driver system.