Character Analysis
Old Rusty
The Tin Man actually has less to do than the Scarecrow and the Lion. He's the "middle child" of the company. Dorothy finds him after the Scarecrow, but before the Lion, and like most middle children, he kinda has to fight for attention. That doesn't make him any less cool than his buddies, or deny him the right to a song and dance number about the trait he wants the most. It's just that once you get past that, the interesting questions become a little thinner on the ground. (Not that we judge. We love him just as much as we love his buddies.)
The Tin Man and Hickory both follow the same basic template as the Scarecrow. Both are mirror images of each other, and while Hickory doesn't speak about the virtues of a gentle heart the way Zeke and Hunk do with their respective missing traits, he still presages his fate as the Tin Man by saying,
HICK: Oh! Oh, it feels like my joints are rusted. Listen, Dorothy, don't let Hunk kid you about Miss Gulch. She's just a poor sour-faced old maid that… she ain't got no heart left. You know, you should have a little more heart yourself, and have pity on her.
Not to mention:
HICK: Someday they're going to erect a statue of me in this town!
(Be careful what you wish for, Mr. I-Spent-Years-Rusted-Solid!)
Again, the Oz version of the character is basically the Kansas guy with a snazzier wardrobe. Like the Scarecrow, he's positively dripping with very quality he's searching so hard to find. No heart? Seriously dude, you cry more than the audience during the first five minutes of Up. Seeing a dead bee in your hand, you're a puddle:
TIN MAN: Oh, see, I killed it. Oh, I killed that poor little honeybee!
You sing songs about loving everyone! You get mopey and depressed any time any of your friends suffers a setback, and like the Scarecrow, you'll cheerfully crawl through an ocean of tin shears to help those who are close to you. Your round metal chest isn't big enough to hold your heart.
We can see that all-important trait in Jack Haley's vocal performance, which he developed by telling bedtime stories to his kids. The Tin Man always talks like he's reassuring a little child: not condescending, but gentle, supportive and with the promise of a lollipop if we all behave. That echoes the character's kind nature and almost lethal levels of empathy. We wonder why he even carries an axe at this point; it's not like he's going to ever use it on anyone.
As with Dorothy's other companions, it's not so much a heart that he needs as belief in himself. And though he's plenty scared by where he has to go, he mans up (Tin Mans up, actually) and does what's required to keep his friends safe. What he earns in the end means so much more than the heart he already has, let alone that silly watch thing the Wizard gives him.
(And seriously, where did the Wizard get that tacky piece of junk anyway?)