Your best bet is to get a portable air conditioner. You can do a bit of research to figure out how many BTU you'd need for the square footage of your apartment.
How Air Conditioners Work (edit): AC Units suck air from within the environment that it's in (for example your living room). And blows "Fresh" or "Cold" Air back into the same environment and at the same time, it blows the heat that is generated from producing the cold air out of the environment (outdoors)
If I have a bottle that is sealed with a pump at the top. Meaning no air can get out, but air can go in. And I start pumping (the same way AC units pump air into a room) Then the bottle will eventually explode because that air needs to go somewhere, the same way a balloon pops when you put too much air into it. A structure can only hold so much air before it can't anymore. This is why an AC unit takes the air from the room you are in and converts it cold air. And why it doesn't draw "fresh air" from the outside. And simply keeps recycling that air, until the room gets cool.
Typically AC units will have a thermostat which will monitor the temperature in the room and shut off when the room has reached a certain temperature. And will turn back on when the temperature eventually rises back up. Because the room you are in, isn't air tight, cold air is going to leak out of the doors, or windows or cracks in the walls.
Depending on your setup, if you set it up at a window, the window will be open, but the cover and vent hole will cover the window like this
I'm not going to assume this window block will eliminate outdoor noise from coming into the house, But I doubt you'll hear it over the portable air conditioner itself. Because it WILL be loud at high speeds. But not as noticeable at low speeds.
So you're either going to have noise pollution from the street by opening a window, or noise pollution from the AC.