This works, as you say, until the air during the night is much colder than during the day. In one summer there were weeks when the air during the night was 27C

This works, as you say, until the air during the night is much colder than during the day. In one summer there were weeks when the air during the night was 27C and it obviously did not cool down. Another downside is that when you do not have mechanical ventilation with heat recovery and your rooms are relatively well built (i.e. air tight) then you are left with bad air quality inside. I think that best is to combine night cooling with mechanical ventilation with heat recovery.