A new custom-designed system for a 3000 ton multi-anvil press has been developed to reach temperatures below room temperature at high pressures. The system was designed to remove heat selectively and conductively from the sample volume through six of the eight tungsten carbide (WC) cubes in direct contact with the octahedral pressure cell. The key components of the system include Cu cooling fins sandwiched between neighboring cube faces and the connected Cu heat exchange chamber through which liquid nitrogen flows. Currently, this system enables us to reach temperatures down to 220 K at pressures up to 8 GPa, but it can be easily modified to retain similar cooling capability at the highest pressure the press can reach (ca. 25 GPa).