[MissileStick]

My recommendations:

Tape up the screens like DonR suggested. Be sure and use blue painter's tape, which won't leave residue (~$3 at a home improvement store).

If you're really adventurous (or a cheap b*****d like me), cover some cardboard with foil and put it in the window. Take it down after the sun goes down and get that cool[er] night air in.

Yeah, the evap cooler really needs to be vented. It will drop the temperature unlike an unvented A/C, but it does so at the expense of humidity. I use, ahem, 'targeted evaporative cooling' with a spritz bottle and the hottest parts of the body, those being the head, wrists, and lower back.

If you must use the evaporative cooler, get a hygrometer and use it when the humidity is low.