A stuck open thermostat will cause the cars engine to run cooler so since the stuck open thermostat will cause the cars engine to run cooler a stuck open thermostat won't cause a cars engine to overheat.
If the thermostat is stuck closed then it can cause the engine to overheat.
The purpose of a cars engine thermostat is to keep the engine operating at the correct temperature and when it's stuck open it allows the coolant to flow too much which cools off the engine too quickly.
When a thermostat is tuck closed the coolant cannot pass through like it needs to when it needs to an then the engine overheats as a result.