My car nearly overheated where temp gauge just touched max temp. Does this mean engine damage? I thought that maybe the thermostat broke so i shut it down and drove later, but it turns out the radiator ran empty but the engine was full of coolant. I drove at high speed thinking the air would cool the engine and the gauge dropped down, but idk if it's because steam might be lower temp than coolant or if it's because nothing was going through the radiator.
This behaviour depends on several factors:
1) the location of the sensor, if it stays in coolant when the radiator is empty it can show the correct reading, usually until the coolant changes to steam
2) if the sensor is not in coolant when the radiator is empty, then it may show the correct T, a high T or a low T but this behaviour is affected by where the sensor is and how it is mounted. Some are in the coolant, others are direct on the head.
As for engine damage, difficult to say - depends how long it was driven for etc. I had a car overheat due to a failed fan - drive home fast on light throttle and it was fine for years after repair. Other cars will warp the cylinder head as soon as overheated is mentioned...
Just note that steam is not “cooler” than the coolant - to become steam it has absorbed more energy, but it is now in a larger volume (1 litre of water forms about 1700 litres of steam...)