If you have a large styrofoam cooler, a supply of ice and a small battery powered fan, duct tape you can made an air conditioner. Look for the show "Hack My Life" or try Youtube for directions.
If the door of refrigerator is kept opened can it cool a room?
Well, remember how the refrigerator cools food.
It removes the heat from the air in the closed, discrete space within the refrigerator and "pumps" it into the kitchen.
So no matter how you rig it up, whatever heat you remove from the room the refrigerator is in goes right back into the room.
If you manage to exhaust the heat into different room, it still won't cool the first room. The cooling unit in the refrigerator is simply not designed to be capable of removing sufficient heat from such a large volume of air as a room to make a significant difference in the temperature of the room.