This is distinctly impractical, but I can't get it out of my head.
Have two buildings, one in Alaska, one in Nevada. Alaska is a polar area, and very very cold. Almost all of Nevada is a really hot desert. Have two long, insulated pipes between them.
In the Alaska building, compress some freon, which heats it up, and allow it to dissipate its heat into the house. Aaah, feels good. When it has cooled, send it down one of the pipes. This pipe ends in the Nevada house, with an expander. As it expands, the temperature plummets, air conditioning the Nevada House. Aaah, feels good.
Meanwhile in the Nevada house, send uncompressed freon up the unused pipe to Alaska, which arrives vaguely tepid. (It will lose some heat no matter how well the pipes are insulated.) Feed this pipe into the compressor, making this an endless heat exchange.
Problems with this system are numerous. One, that much pipe is insanely expensive, and two, it crosses an international boarder in Canada, or is an undersea pipe at some point. Either will exponentially increase the expense. Two, the energy burden is in Alaska, which has fewer options for electricity. Three, I'm not sure that much freon exists on earth. Four, if the freon leaks at any point, it will be hard to detect and a major environmental disaster.
I'm not even completely sure that it would be more energy efficient than just a heater in Alaska and air conditioning in Nevada.
International readers are encouraged to substitute closer cold-and-hot locations for this, like European readers substituting "Alaska" with "Finland" and "Nevada" with "Italy."
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