Exergo-thermo-volumes provide a novel approach to simultaneously quantify the thermofluidic performance, operational cost, and environmental sustainability of a given thermal management system. In this work, we demonstrate the use of exergo-thermo-volumes to optimize the cooling infrastructure of a data center along the above criteria. The paper begins with an overview of the methodology and its use in the form of multi-component network models. Using such a network, a performance assessment model is proposed that takes into account the key vectors of thermofluidic performance, energy efficiency (operational cost), and environmental sustainability of a given system. We then apply the methodology for data center management. By applying to an example case study of a traditional data center, we show how an exergo-thermo-volume network can be used to gain insight into the design and operation of the compute as well as cooling infrastructures. Differences in infrastructure performance across various operating environments are discussed, and an optimal design that trades off key vectors of thermofluidic performance, operational cost and environmental sustainability is developed. The paper concludes by reflecting upon a generalized design and management strategy for sustainable design of future data center architectures.