A radiator overflow tank collects the expanding coolant that is heated by the engine and recycles it back into the coolant system once it loses enough heat. The radiator overflow tank works in conjunction with the radiator cap to protect the engine and prevent coolant loss due to overflow, according to HowStuffWorks.
The radiator overflow tank serves as the reservoir for engine coolant that is heated to its boiling point and would otherwise rise up and out of the radiator. Working in conjunction with a thermally activated spring built into the cap, the overflow tank creates a closed cooling system that is much more reliable and practical than previous designs. As the temperature and pressure rise to the coolant's boiling point under pressure, the cap spring activates and allows the heated liquid to flow up and into the overflow tank. The fact that the system is under pressure means that the liquid reaches a higher temperature before boiling, further increasing the effectiveness of the system.
Prior to the advent of effective closed systems, large mechanical fans were used to cool most engines, though they had their drawbacks. Mechanical fans were ideal for driving at low speeds but actually cooled engines too much at high speeds. The solution was the advent of electric fans that turned on and off as the engine temperature rose and fell. Most modern vehicles and mechanical engines employ a combination of an electric fan and a closed cooling system.