Gas bubbles rise with increasing frequency and the temperature sinks lower and lower. Even way below 100 C, the water is still boiling. The released steam does not appear to have any effect on the bottle.
The bottle is full to the brim with water, so there is very little air in the system. The heated water takes up a certain amount of space. The substances usually expand when heated and shrink when cooled, hot water takes up more room than cold water. So if you cool the water by placing ice cubes onto the bottle top, the water contracts right underneath it. A free space is created. In our normal, earth conditions, water has to reach 100 Celsius to boil. The main reason for this is the ambient pressure of the air onto the water surface, inhibiting evaporation. That is why water needs so much energy before it will boil. But in our bottle, an empty space has been created in which there is virtually no pressure on the water, so it can become gaseous much more easily. It boils at below 100C.
This works until the space has filled with steam, which then puts pressure on the surface of water. Further cooling with ice cubes then condenses the steam and again creates the low pressure space in the top of the bottle. The process repeats and even amplifies, as the water is consistently losing heat and takes up less and less room. Evaporation can take place down to ca. 45 Celsius.
The answer to the question in our introduction is, of course, at sea level. A hungry explorer on Everest will have a hard time cooking his egg. The air pressure at 8,848 meters is much lower than at sea level and water boils much more quickly, namely at 70Ã