Article says it works all the time.
During nightime, the temperature differential may be reduced, but it certainly doesn't go to zero. It's colder up there at the top. My main concern would be the structural stability of such a tall object, and its potential vulnerability to extreme weather, accidents or intentional destruction. Must the tower be made of glass, or could it be a more conventional material like corrugated steel or aluminum panels bolted to a steel frame? It's a very elegant concept. But in a world where neighbors don't want to live near giant windmills, nimbyism might be a serious problem.