Instead of a taking a shower or shampooing one's hair in the morning (generally due to tardiness), simply wearing a baseball cap over one's ratty hair.
Dude, I was late for class, so I had to take a hat shower.
When someone wears a hat to rid themselves of bed head because they didn't have time to take a shower.
Person 1: Dude i was running so late today i only had time to take a hat shower. Can you tell?
Person 2: Well you kinda smell but you look oh so fine. No homo