Let's further assume that I'd rather have the room cooler than 30C. Also, regardless of which direction the fan will blow, there also needs to be another place

Let's further assume that I'd rather have the room cooler than 30C. Also, regardless of which direction the fan will blow, there also needs to be another place for air to move into and out of the room. So let's also assume that the window is the only opening, but the fan doesn't fill the opening produced by raising the window. One more assumption: I can point the fan with freedom in most any direction once it's placed. I believe I'd pull the cooler air into the room by having the air blow in. I might also point the fan up and away from the other side of the window (up because I want to disturb/displace the warm air higher in the room; away from the non-fan side because I don't want my cool air to be pushed right back out.) I don't want to cool the warmer air, I want to replace it with cooler air.