Some will break themselves. When we’ve allowed a hen to stay broody (no real eggs under her) she will sometimes take 2 weeks or 3-4 weeks (normal hatch time). If you let her wait it out, you should make her go out for a bit each day for food and water.
We don’t usually allow them to stay broody. So, the cage thing can work great bc their fluffy butts can’t stay warm like they would on a nest. I’ve heard some people will put them halfway (bottom half) in cool-cold water for a bit to help cool them down and sometimes this helps -but, if they are heavily feathered or it’s cold out, a chicken needs help to get dry (towel+hairdryer which they surprisingly like). Their underfluff stays wet otherwise and areas like between legs have a hard time drying.
Our usual method is to separate them from the flock. They can see but cannot join the flock, which is somewhat distressing to them . Right now, as I type, four hens of one breed are all broody, and are together in a protected pen that is near but not with the flock. They are less likely to settle into a nest (no nest boxes in this pen) and it helps them to loose their broodiness. I say that, but one of these four was in this pen a week ago for three days (with two other broody hens) and apparently wasn’t fully broken and within a few days was back to being broody.