Second Prototype model
This model version addresses the many issues related to the distribution of light and different times of the day taking into account the temperature as well.
Final Model
Interior birds-eye view
Side View
Lighting
This will be our base ambient lighting model from this perspective.

As the sun rises in the morning the light enters from the light shaft window as well as the one below it.

As the sun rises the light hits the shaft and creates further bounce light from the ceiling thus adding more natural light entering during the morning

The sunlight as show slowly diminishes as it rises above the roof however there may still be a slight gap where the light can hit the person if standing; an adjustment to the light shaft or roof lip may be required to prevent this.

As it reaches noon, the amount of direct light entering the room is minimized to prevent further heat from entering the room. As a compensation natural light is entered through a translucent skylight creating a softer diffusion of lighting.

This is further assisted by the wall of the angled room that, when hit by the afternoon sunlight, provides further bounce light which will be transmitted through the skylight.

As a preference the user can choose to have blinds for the lower windows allowing the blockage of direct sunlight if working at the desk or doing other activities without the sun hitting the face.
Here is a morning shot of the sunlight entering the room with blinds this time.

Shot at noon, showing better distribution of soft light coming from the skylight

And most importantly once it reaches afternoon, this is when the direct light is most unwanted, only transmitting bounce light from the roof wall entering via the skylight. (The light coming from the corner is just a gap within the model).

The angled window at the edge of the room, other than being an aesthetic choice, was designed with rejecting the most amount of direct lighting according to the direction of the sun. This also can provide the user with a wide view from the room which overlooks a road.