Building systems such as heating, air quality control and refrigeration operate independently of each other and frequently result in temporally correlated energy demand surges. As peak power prices are 200-400 times that of the nominal rate, this uncoordinated activity is both expensive and operationally inefficient. We present an approach to fine-grained coordination of energy demand by scheduling the control systems within a constrained peak while ensuring custom climate environments are facilitated. The peak constraint is minimized for energy efficiency, while we provide feasibility conditions for the constraint to be realizable by a scheduling policy for the control systems. The physical systems are then coordinated by the scheduling controller so as both the peak constraint and the climate/safety constraint are satisfied. We also introduce a simple scheduling approach called lazy scheduling. The proposed control and scheduling strategy is implemented in simulation examples from small to large scales, which show that it can achieve significant peak demand reduction while being efficient and scalable.