The title is also a reference to the Elvis Presley song "Burning Love".
Homer's new job as the author of fortune cookies assures Mr. Burns that love is on the horizon. Mr. Burns finds it in a woman named Gloria, whom he loves so much that he wants to marry. But as he proposes to Gloria, her ex shows up - which happens to be Snake, and he's just broken out of prison.
The Simpsons take in the sights and sounds of Chinatown and dine at a Chinese restaurant. As they finish the meal, Homer opens a fortune cookie and reads his fortune aloud. When Homer voices displeasure with his fortune, and informs the restaurant manager it doesn’t make any sense, he makes up some of his own. Impressed, the manager hires Homer to write fortunes. At home, Homer thinks up of a whole bunch of fortunes while Lisa is trying to type them up on a Chinese typewriter (which is mainly her poking the button 市). One evening, Mr. Burns orders a Chinese takeout. His fortune reads, “You will find the love of your life on flag day.” Inspired, Mr. Burns has Smithers accompany him for a night on the town. But their attempts at finding Burns a mate prove fruitless.
As the two men make their way back to Mr. Burns' car, he sees a police officer ticketing it. The officer is a woman named Gloria, and, finding her attractive and vivacious, Burns asks her out to dinner. Despite their age difference, Gloria accepts Burns’ offer to go out. But as the date progresses, Gloria has second thoughts about dating the old man. Thinking quickly, Burns tells Gloria that he and Homer are old friends who have enjoyed many youthful exploits together. Homer lists Burns’ various “accomplishments,” impressing Gloria and rekindling her interest. Later, Homer accompanies Burns and Gloria on their next date, which includes a stop at a disco bar. Burns and Gloria retire to the mansion, where Burns injects himself with a powerful aphrodisiac. Before Homer leaves the mansion, he injects himself with the stimulant, then returns home and makes love to Marge.
On their next date, Burns and Gloria go bowling. Homer again accompanies them. When Gloria sticks her fingers into a ball, she notices something unusual and pulls them out. On one of her fingers is a large diamond ring. Mr. Burns proposes…and Gloria accepts. A few moments later, Snake enters the bowling alley, gun in hand, intending to rob the cash register. Instead, he notices Gloria (she is Snake's old flame) and insists they run off together. When Gloria refuses, Snake kidnaps her. Homer comes to Gloria’s rescue, but he is taken hostage as well, and the threesome drive off in Mr. Burns’ car. Snake takes Homer and Gloria to his hideout where Gloria and Homer are tied to their chairs and taunted, but the police pinpoint their location thanks to the anti-theft system concealed in Burns’ vehicle.
Inside the house, Homer tries to burn the rope binding him with the fire in the fireplace, but ends up setting the whole house on fire. However, he manages to burn the rope off and runs out of the house, Snake following him. Burns decides to save Gloria himself, who is still bound and trapped inside, and races inside the burning building. He appears to have rescued Gloria, but then it is revealed that Gloria saved Burns. As Snake is rearrested, Gloria starts to admonish him, but then finds herself falling for him. She breaks up with Burns and throws herself on to Snake. Burns is disappointed as to how she couldn't love him, saying that he is "evil" as he walks down the road with the Simpsons.