What about making a heat exchanger?

Set up a freezer in the landing. (or wherever, so long as it's radiator is outside the room).
Wind some copper tubing into a coil and make sure a fan is blowing across the coil.
Attach a flexible, insulated tubing like surgical tubing to the ends of the coil and run those ends out of the room.
Attach another bit of copper tubing to the ends of the flexible tubing and set that in the freezer
Add some water & anti-freeze to the tubing as your working fluid.

A pump may or may not be necessary. If the coil and fan in the room is lower in elevation than the freezer, convection will drive a flow. Probably convection wont be enough, so a pump is likely to be necessary.

The freezer can be replaced with a cooler full of ice, but the freezer requires less maintenance.