Current lunar-based Fission Surface Power (FSP) Systems that will support sustained surface outposts consist of a nuclear reactor with power converters, whose waste heat is transported to radiator panels to be rejected to the environment. The current approach is to transport waste heat using a heavy, pressurized water cooling loop. For each 20 kW of heat rejection, the current water cooling loop components weigh approximately 52 kg due to the large flow rate of water, the large pressure drop, and the pump and other components. Our innovation is a novel Waste Heat Transport System (WHTS) that combines Creare's lightweight radiator technology with a Lightweight Cooling Loop (LCL). Using our approach, we estimate that our LCL will reduce the cooling loop system mass by 60% compared to the current approach. Our approach will have a reduced system pressure, resulting in decreased plumbing size and weight, and eliminate the need for a mechanical pump, increasing system reliability. During the Phase I project, we will establish the feasibility of our innovative, Lightweight Cooling Loop (LCL) by fabricating a fully operational, subscale prototype and testing it under prototypical conditions. During the Phase II project, we will design, fabricate, and deliver to NASA a prototype LCL for integration with our ultra-light radiator.