There isn't much canon on Caranthir's life that I am aware of. His mother-name is Morifinwë, literally dark-Finwë. This is attributed in HoMe XII to his dark hair, but I find that explanation unconvincing since nearly all Noldor were dark-haired. I have always wondered whether the name came from having a darker temperament than most people.
"The incident with Angrod" is canonical, though I've left out the details for the purpose of space here.
But Caranthir, who loved not the sons of Finarfin, and was the harshest of the brothers and most quick to anger, cried aloud: 'Yea more! Let not the sons of Finarfin run thither with their tales to this Dark Elf in his caves! Who made them our spokesmen to deal with him? And though they be come indeed to Beleriand, let them not so swiftly forget that their father is a lord of the Noldor, though their mother be of other kin.'
Then Angrod was wrathful and went forth from the council. Maedhros indeed rebuked Caranthir; but the greater part of the Noldor, of both followings, hearing his words were troubled in heart, fearing the fell spirit of the sons of Fëanor that it seemed would ever be like to burst forth in rash word or violence. ("Of the Return of the Noldor," The Silmarillion)
Caranthir's lack of diplomacy shows up in his dealings with the Dwarves:
And thus it was that Caranthir's people came upon the Dwarves, who after the onslaught of Morgoth and the coming of the Noldor had ceased their traffic into Beleriand. But though either people loved skill and were eager to learn, no great love was there between them; for the Dwarves were secret and quick to resentment, and Caranthir was haughty and scarce concealed his scorn for the unloveliness of the Naugrim, and his people followed their lord. ("Of the Return of the Noldor," The Silmarillion)
Incidentally, this is the passage that gave me the idea that Caranthir was a craftsman. I know that in HoMe XII we're told that "[Curufin] alone showed in some degree the same temper and talents" as Fëanor. If you take HoMe as canon (I don't), this can be read as saying that Curufin had the temper and talents. I like to imagine others had a scientific skill set but just not his temper, and Caranthir seems to fit the bill. I think his accomplishments can be more attributed to diligence than genius, anyway.
Some of you may notice two allusions to the Hobbit: Caranthir's disbelief that anyone would really fight "a war for gold," and the dwarves' charge that Caranthir "horded his gold [...] and never spent a brass ring." That's not an accident. While I really enjoyed developing a craftsman Fëanorian and showing him as a bit of a geek, this story was as much inspired by the Hobbit as the Silmarillion. I always felt Thranduil was unfairly maligned by the dwarves and Bilbo, and that it was a really good thing that he had accumulated all that wealth. How much worse would things have been for the people of Laketown if he lived richly and didn't keep his treasures in reserve?