After dousing the flames and cooling operation, the civil defence handed over the site to the police.
He was airlifted from the oil field to the hospital.
First Corporal Tariq Abdullah Ali Al Hawai accidentally fell from a "hole" on the fourth floor of the building.
No casualties have been reported.
Police confirmed that the cause of the death was cardiac arrest.
Scores of worried and anxious parents waited outside the campus gates for nearly an hour in scorching temperature.
She crossed the road from a non-pedestrian crossing area.