Very good question asked. I know the following consequences:
Detonation: When the engine overheats, it starts to detonate and thus the engine loses power. And also, if the detonation continues, it damages rod bearings and rings.
PIsto damage: When the car gets hotter and hotter, the Pisto in the engine get swelled which results in no expansion which damage the cylinders.
Blown Gasket: Engine overheating also results in blown head gasket. Because of the heat in the engine, the aluminium gets swelled because of the same which blows the head gasket and adjacent cylinders as well.