Often people ask questions that superficially sound like this about how to get something for nothing, violating thermodynamics. The good news is that this isn't one of those questions. The process is definitely possible.
The bad news is that the simplest schemes I can think of for driving circulation using a temperature difference all work upside-down, with the hot part on the bottom. It's not hard to design a simple device with some working fluid that boils a little below room temperature that will drive itself around in a closed-loop still-type set-up if the bottom part is warm and the top part is cool. (Some alcohols would probably work well.) Unfortunately you have the opposite situation, which raises trickier engineering problems. Maybe some reader can help on this.
It would help to know if the main goal here is to run an electrical generator or to circulate fluid, or both. How much output of either type do you need?
For fluid circulation, you might be able to use a Stirling engine (http://en.wikipedia.org/wiki/Stirling_engine
) driving a pump. If the pump pulled cool fluid up by one side of the engine and warmer fluid returned by the other side, then it would power itself, once you got the flow going. You could also use separate loops for the cool fluid and the warm fluid, each with it's own pump. Or you might be able to just use a loop for the cool fluid, with fins to pick up heat from the air. (As you know, but some readers might not, the source of the power is that the ground and the air are out of equilibrium, not some magic in the engine.)
If the goal is to get some electricity, perhaps it would make sense to directly use thermoelectric devices (http://en.wikipedia.org/wiki/Thermoelectric_generator
), which are sort of glorified thermocouples. A temperature difference applied to such a device directly generates dc voltage, and can supply a small current. Of course, in order to keep one side cold and the other hot you might want to use some circulating fluid anyway, which means you might still want a pump, driven either by that Stirling system or by a little of the electrical power from your thermoelectric elements.
(published on 03/10/2011)