The disclosed embodiments relate to a system that controls cooling in a computer system. During operation, this system monitors a temperature of one or more components in the computer system. Next, the system determines a thermal-headroom margin for each of the one or more components in the computer system by subtracting the temperature of the component from a pre-specified maximum operating temperature of the component. Then, the system controls a cooling system that regulates an ambient air temperature for the computer system based on the determined thermal-headroom margins for the one or more components. In some embodiments, controlling the cooling system additionally involves minimizing a collective energy consumption of the computer system and the cooling system.