Down here in the stifling south we figured it out a long time ago. Old "cracker" houses were vented at the top and bottom which allowed hot air to escape and be replaced by cooler air sucked from the shaded lower levels of the house. Go buy a special window fan which has movable sides to fill all the window space. Don't just stick a regular fan in a window, it'll just suck hot air in thru the window around the sides of the fan.
Put the fan on exhaust and open all doors to the cooler lower levels, but close all other windows in the room and on the upper floor if possible. Otherwise you'll just suck in more hot air.
Stay warm.
6
ps: search "cracker house" for a better description of how it works.
