A low-power, large-scale, and efficient cooling system has been developed to cool lithium-drifted silicon [Si(Li)] detectors distributed in a balloon payload of the General Anti-Particle Spectrometer (GAPS). The system is composed of a multi-loop heat pipe, a reservoir, auxiliary heaters, and a backup pump, all of which are based on state-of-the-art thermal control technologies. Basic functions of this unique system have been verified by environmental testing, in-flight tests, and numerical analyses. This novel cooling concept can be applied to similar situations where distributed heat sources must be cooled.