Hi, small and probably dumb question, is there a way to cool air in a room without having to extract the hot one ?
Do you mean do you have to change the air in the room to cool it? If so, the answer is no. You do have to extract the heat though.
So you want something like a car where you can change it from recirculate to outside? I've never heard of that for homes, but I wouldn't be surprised if someone did it.
Absolutely, there is no need at all to remove or add air to a room or vehicle to cool the air inside. You cannot, however, cool air without removing the heat from it. You do not cool air, you remove heat.
Exactly...this is the principle behihd (what people in Arizona call) "swamp coolers", aka evaporative coolers.
The only way to cool air without removing the heat to an outside place would be to introduce something cold into the room... i.e. if you put a bucket of ice in there it would cool the room down. The only other way would be an endothermic chemical reaction but both those solutions "run out".