The cartoon takes place at Bedlam Manor, in 17th Century England. Sam, Duke of Yosemite finds out from his big-nosed servant that his uncle, the King, has decided to cut off his allowance. Sam punishes the servant for this message by giving him the nose-in-the-book penalty (slamming a heavy book on the servant's big nose). Sam is desperate for money. Bugs Bunny comes to his door offering one million pounds to a mild-tempered person. Whenever Sam loses his temper, a small fraction of the one million pounds will be deducted, the size of the fraction depending on what Bugs thinks it suits. Sam welcomes Bugs into his home, anxious to receive the one million pounds.
Bugs plays the role of an annoying house guest, presumably to test Sam, this naturally provokes Yosemite Sam to lose his temper and losing more money. Bugs asks Sam for multiple items at dinner. Each time he is asked for something, Sam loses his temper, and shouts out phrases like “Rackin’ Frackin’ Varmint Rabbit”. Each time Sam loses his temper, he loses money as well. This gets him even madder, causing him to lose his temper over and over again. Going into a closet to rant and rave doesn't help as Bugs can hear him (causing Sam to lose his first £300, then 400 when Sam shouts "£300?!"), so Sam has to run outside to rant and rave.
That night, Bugs keeps provoking Sam by playing the piano and singing his version of "Jeanie with the Light Brown Hair" obnoxiously while Sam is trying to sleep only for him to say "Stop that music, ya crazy rackin', frackin', varmint rabbit!". After Bugs deducts some more money for Sam losing his temper, Sam asks Bugs to sing him to sleep by playing "Brahms' Lullaby." Bugs then becomes a one-man band and ticks off Sam even more, though Sam pretends to believe that he likes it.
Next morning, Bugs hogs the bathroom and when Sam knocks on the door and demands him to "Get out of there!", Bugs opens it quickly and accidentally smashes Sam between the door and the wall (Bugs strangely doesn't deduct from Sam's money this time, presumably because he didn't see him or because he thought it was someone else). When Sam shouts at him to get out, Bugs deducts even more money (£400 and 35 shillings this time). Already furious, Sam pounds his head on the piano, making Bugs think Sam's playing a song. Realizing he's not going to have any money left if the temper-money deductions keep up, Sam gets an idea to kill Bugs in order to receive all of the one million pounds – an idea he plans to make look like an accident.
Each time Sam tries to kill Bugs, it backfires, causing Sam to fall into his own trap and get injured. First, he saws a hole in the floor outside the bathroom door and tries to get Bugs to come out by telling him somebody wants to see him, but Bugs orders Sam to tell whoever it is to come back the next day as he'll be in the bathroom all day. This makes Sam mad enough to bust into the bathroom and push Bugs out, only to fall through the hole intended for Bugs and land in the river below and curse while falling. When Sam returns and Bugs tells him he's done with the bathroom, Sam rushes at him to strangle him, but falls through the hole and into the river again, again cursing the entire way down.
Later, Bugs climbs up a really long staircase (“The Alps have got nothing on these stairs for climbing.”). At the top, Sam, dressed in a suit of armor, tries to chop off Bugs' head with a double-bladed axe, but Bugs ducks and he falls down the stairs. While falling down the stairs, Sam continues to rant, curse and rave, and Bugs continues the deductions (all of which strangely weren't mentioned).
Finally, the next day, Sam gets control of his temper. He tries to show Bugs this by having his servants physically abuse him by kicking him (the big-nosed servant from earlier), throwing pies in his face, and hitting him with a rolling pin (presumably punishment for his actions). Bugs looks at the camera and says, “I haven’t got the heart to tell him he’s used up all the money” as the cartoon fades out.
The ABC version of this cartoon shortens the part at the end of the cartoon where Yosemite Sam shows Bugs that he "...don't get mad no more" and lets his servants kick him, hit him in the head, and slam a pie in his face (before Bugs asides to the audience that he doesn't have the heart to tell Sam that he lost all his money).
"From Hare to Heir" is available, uncensored and uncut, on the Looney Tunes Superstars DVD. However, it has been cropped to widescreen. Which caused anger among Looney Tunes fans and collectors. The video below is a remastered fullscreen version of the cartoon (with some logos).