This requires a bit of planning, but works -

Get the largest container (open top) that you can fit into your freezer, and use it to freeze some water.
Later...
Take the container of ice upstairs and place it in a strategic position, so you can direct your fan so the air flow 'skims' the surface.

The ice, and later cold water, will cool the air which will be circulated round the room.

You can thank me later.