It is unlikely that a cracked distributor cap would cause an engine to overheat. The distributor cap is responsible for distributing the electrical current from the ignition coil to each of the spark plugs in the engine. While a cracked distributor cap can cause engine performance issues, it is not typically associated with overheating.
External coolant leaks, a faulty thermostat, and an inoperative fan motor are all common causes of engine overheating. External coolant leaks can cause a loss of coolant, which can lead to overheating. A faulty thermostat can get stuck in the closed position, preventing coolant from flowing through the engine and causing it to overheat. An inoperative fan motor can prevent the cooling fan from working properly, which can cause the engine to overheat.
It's important to note that there can be many different causes of engine overheating, and a proper diagnosis is necessary to determine the root cause of the problem.