What happens to an enzyme's structure as it exceeds the typical human body temperature?
Depends on the enzyme I guess!
As you're talking about the human body, I'll assume you mean human enzymes as there are enzymes that work at very high temperatures just fine.
If an enzyme exceeds its optimum temperature, the molecules within its primary structure vibrate so much that the shape of the active site changes and it becomes 'denatured'.
This means it can no longer bind its substrate (lock and key hypothesis) and will not function as required. This process can be reversed if cooled back down although the protein doesn't always reform into its original conformation.
I like to think of an enzyme as a 'Pac-Man' shape with the mouth as the active site. If denatured, the mouth will not be the right shape anymore.