Window A/C unit venting

I have a two story home, with a window A/C unit upstairs and central air downstairs. Obviously, the upstairs of the home (with a bedroom and bathroom only) is MUCH, MUCH warmer than downstairs, even with the window unit running.

Should I place a fan in one of the upstairs windows (facing outside) to pull the hot air out of the rooms? It does not have any type of return venting so the heat just stays in the upstairs rooms.

Thanks