Answer
Leaving the refrigerator door open is ineffective, but a cooler full of ice will cool the kitchen.
Work Step by Step
Leaving the refrigerator door open is ineffective because the heat that is drawn out of the “inside” is soon expelled to the “outside”, which is the same space. Moreover, the refrigerator motor itself exhausts even more heat, so the net result is heating up the kitchen.
Bringing in an open cooler of ice will work. The ice takes in heat from the room, and melts due to the rise in its internal energy. It turns into water at the same temperature. The net result is a cooling of the room.