The page image that you can see is actually for Oscar the Cat. He's supposedly quite rude and irritable towards most people- except ill and dying patients. He goes up to them and lets them pet him as much as they want.
Edge. He may be somewhat sociopathic, arrogant and vicious, but he did show that he cared for his (kayfabe) wife Vickie Guerrero, and despite being turned on several times, always would help out his best friend Christian.
William Regal. A pompous British aristocratic type for most of his career. His heart of gold was shown when Eric Bischoff's "special" nephew, Eugene, came into WWE. Bischoff wanted Regal to break his spirit in the hopes he'd quit, but once Regal saw Eugene could actually wrestle, he became very supportive of him.
Mark usually falls into this trope, although he does sometimes act like a straight up Jerkass
In The Gamers Alliance, several characters who act rudely are shown to have a hidden heart of gold and that deep inside they really do care for others, or at least grow into people who start caring about other things than themselves. Examples include the cynical mage Raistlin II, the old merchant Kusobaba, and Sultan Khalid.
Gulliman, the primarch of the Ultramarines was a hard ass, but he legitimately cared about the people he ruled and established the government of the Ultramarines mini empire around the idea of meritocracy (it is theoretically possible for a peasant to one day rise and become chapter master thus rule the empire). His actions have resulted in one of the best places (and least corrupt) to live in the entire Imperium.
The default characterization of many Paladins in D&D. Arrogant and self-righteous, yes, but the "righteous" part does apply, and as written, Paladins have a soft spot for anyone in need.
Benedick in Much Ado About Nothing is a fountain of snark who pretends to be a He-Man Woman Hater, but as soon as he is convinced that Beatrice is in love with him, he softens up instantly. He is also the only male character (other than the friar) to believe in Hero's innocence when she is accused of cheating on Claudio, rather than siding with his male friends as even Hero's father does.