I was watching one of those mega-engineering shows a few days...

I was watching one of those mega-engineering shows a few days ago about modern very high rise building construction. It occurred to me could a central 'hole' left in one of these buildings act as a vent-stack for EVM's technology to power the building? Would there be enough heat differential without the surrounding greenhouse? Leaving a hole up the building could be a cheap way of building a tower.