It's very tempting to believe, when you stand next to an open window and feel the breeze on a hot summers day, that it's cooling you down. It may be cool as you stand there, but if the temperature outside is higher than inside, and you happen to be in a well-insulated, airtight house, and it's likely to be over 30 degrees every day for the next month with a chance of a few nights staying above 25 degrees, then you really don't want the windows open when it gets hotter.
The heat exchanger in the ventilation system will do a much better job than the windows at keeping it cool. If it's 30 degrees outside and 25 degrees inside, the air coming in through the windows will be at 30 degrees, but the air coming in through the ventilation system will be a little over 25. It may be more humid, but that's another issue. Humidity could make it feel one or two degrees warmer, but not five.
Of course, the air coming in through the window may be cooling you down by helping evaporation and blowing heat away from your body, but even if it is, the heat is going into the house and will be there for you later.
Then there's the effect of air at velocity expanding into the room.
I remember this from the day of the first airtightness test, 9th August, 2011. It was a hot one, 31.6 degrees outside, according to the test report. It was 31.3 inside. The house was still being built then, so the windows were usually closed at night and left open during the day. We now do the opposite.
For the airtighness test, the windows had all been closed. They had fixed a fan to one of the windows, then blew a lot of air out until the pressure dropped about 50 pascals below the pressure outside. Then the fan switched off and the machine started to measure the pressure go up as the air leaked in again, and that was our chance to go around the house searching for places where air was getting in.
You could feel little jets of cold air coming in at the corners of some of the windows. I remember wondering at the time why the air should feel cold when it was hot outside, inside, and presumably in the wall between. Now I realise it was the air expanding. The same amount of heat. Bigger volume. Lower temperature.
So the same thing is probably happening, to a lesser extent, when the window is open and air is rushing in to a large room. But when the air stops moving and settles at the ambient pressure, which is very close to the atmospheric pressure, no coolth has been gained. Or rather no heat has been lost, since "coolth" is neither a word in English nor in science.
It would be nice if this effect could be used in some low tech way, with fresh air outside somehow increased in pressure so that it would come inside at a desirable temperature and pressure, and genuinely cool the house. Something more sophisticated than an open window but less than an air conditioner, which in fact uses the same principle but with a coolant rather than air.