It exists, it's called a geothermal heat pump / ground-source heat pump.
[0]https://en.wikipedia.org/wiki/Stack_effect
[1]http://www.northerntool.com/shop/tool/product_200510953_2005...
I am wondering why cycling air directly with no heat pump isn't used more often.
Even with a heat pump, air has to be passed over the evaporation coils anyway.