Video of the incident shows the suspect taking almost 15 minutes to heave the cooler away in the Fort Lauderdale suburb of Oakland Park.
He struck at 4:09am on Thursday 2 April after walking up to the Chevron convenience store to find the clerk snoozing on the other side of the window.
Footage shows him looking closely at the employee for a minute and then into the camera and before making an obscene gesture.
The sneaky thief examines the cooler from various angles before slowly dragging it away from the wall, so as not to rouse the sleeping cashier.
Dennis Norman, 25, of Fort Lauderdale, was arrested on Wednesday and charged with grand theft, said the Broward County sheriff.