Difference between Question of the hour and Question of time

question of the hour—currently the most debated issue:

• It is the living question of the hour, and not the dead story of the past, which forces itself into all minds.

question of time—said of smth. that is thought certain to happen sooner or later:

• Baby-sitting having become firmly established, it was only a question of time before somebody offered to provide a similar service for dogs.