A thermal management system for transferring heat between fluids includes a thermal transport bus through which a heat exchange fluid flows. Additionally, the system includes a heat source heat exchanger arranged along the bus such that heat is added to the fluid flowing through the heat source heat exchanger. Moreover, the system includes a plurality of heat sink heat exchangers arranged along the bus such that heat is removed from the fluid flowing through the plurality of heat sink heat exchangers. Furthermore, the system includes a bypass conduit fluidly coupled to the bus such that the bypass conduit allows the fluid to bypass one of the heat source heat exchanger or one of the heat sink heat exchangers. In addition, the system includes a valve configured to control a flow of the fluid through the bypass conduit based on a pressure of the fluid within the bus.