Is this violent?

I would guess mainly the coffee scalding scene (which is pretty horrific, even if it doesn't directly show the act, although they later show the ruined face), and the fact that women are often the victims. There is also a fatal car-bomb, and a woman getting burned with cigarettes, and of course some fisticuffs and people getting shot. Also someone gets raped, tortured, and killed, but none of that is shown on film. The film just has a rather cruel atmosphere. Probably one of the more violent pre-1960 crime films I've seen, although its not especially graphic by todays standard it still manages to convey an impact.

It's considered to be among the most violent of film-noirs. However, as mentioned, most of the violence occurs off-screen. The same goes for another great film-noir, Kiss Me Deadly. That is another violent film, even though we don't see much of it on-screen.

However, if you compare The Big Heat or Kiss Me Deadly to some of the great film-noirs of the '40s, it's much more violent and deals with even stronger plotlines than The Maltese Falcon or Double Indemnity (for example).

"Sometimes nothin' can be a real cool hand."

Without wanting to spoil it, almost every death we encounter is horrendously violent in some way. What gives the protagonist his jolt is a death close to him, and it's nasty.

Fritz Lang brutal though, you have to to love it :)