Cooling systems and methods for cooling in a power plant using a phase change material. In one embodiment, a phase change material container includes at least one phase change material which may be in the form of a slurry; and at least one conduit for transporting the fluid through the phase change material when located in the phase change material container. The system may also comprise an air flow chamber; and a phase change material flow system including a pump for pumping phase change material from an outlet of phase change material container, to at least one phase change material spray nozzle. The phase change material flow system is configured to ensure that solidified phase change material is returned to the phase change material container.