High-performance cooling is often necessary for thermal management of high power density systems. Both human intuition and vast experience may not be adequate to identify optimal thermal management designs as systems increase in size and complexity. This paper presents a design framework supporting comprehensive exploration of a class of single phase fluid-based cooling architectures. The candidate cooling system architectures are represented using labeled rooted tree graphs. Dynamic models are automatically generated from these trees using a graph-based thermal modeling framework. Optimal performance is determined by solving an appropriate fluid flow control problem, handling temperature constraints in the presence of exogenous heat loads. Rigorous case studies are performed in simulation, with components having variable sets of heat loads and temperature constraints. Results include optimization of thermal endurance for an enumerated set of 4,051 architectures. In addition, cooling system architectures capable of steady-state operation under a given loading are identified.