In an ideal world.
If it's only the sun you need then put the big light source on a circular track and move it across/around the window.
If you have to go in to night then use the same lamp and a few meters of gel start with CTO and grade over to CTB gradually. The moon wouldn't normally act continuously like that but as a trick it will work.
If you want to use the sun then pictulate it like time-lapse but more beautiful. If you use the sun, what happens if it gets cloudy half way through the day?