Reducing the operating energy costs of commercial buildings in the presence of complex tariff structures is an important problem facing several facility managers. In this paper, we explore the use of a data driven pre-cooling methodology for achieving this outcome. Our contributions are twofold. First, we propose a 'gray box' approach to model the building thermal dynamics that imposes minimal data requirements from a building management system (BMS). Second, we illustrate how the model can be used to evaluate various 'what-if' pre-cooling strategies to reduce peak demand by applying it to data obtained from a large commercial building located in Australia. The proposed approach enables facility managers to take informed decisions for improving the energy and cost footprints of their buildings. This paper sets the ground for a deeper study into using pre-cooling, driven by our gray box model, for energy cost optimization in commercial buildings.