[icanhackit]

I proposed an idea for cheaply cooling tall office buildings to a mechanical engineer and structural engineer that they thought was interesting but we were all a little drunk at the time so we didn't even get to calcs on a napkin stage...

It's a very old and widely used concept that just needs scaling up - using the Stack Effect [0] by turning the core of a building into a giant chimney that extends/protrudes past the populated floors to maximize temperature difference. The elevators would run along the exterior of the building to free up the space in the core, with the added bonus that you're not limited by the space in the core and can have an array of elevators to move lots of people.

You could even pair it with water reservoirs to create a sort of low-tech evaporative air-conditioning. Bonus points for using the extrusions/paneling on the building exterior for catching rain water and storing it in the reservoirs.

I think the main issue is that it would need some proper fire safety modelling to make sure you don't create a giant blow-torch if someone in the lower suites burns some toast or leaves a dodgy floor heater running overnight.

Disclaimer: I am in no way qualified to say whether this would work

[0] http://en.wikipedia.org/wiki/Stack_effect