There can be false alarms with hens appearing to be going broody. It's important to know and be able to identify broody symptoms. Lingering on a nest does not necessarily mean a hen is broody.
As a way of demonstrating a hen that is pre-broody but not yet all the way broody, I'll tell you about my tiny Sicilian Buttercup Saffron. She's only slightly over a year old. A bit over a month ago in late October, she began clucking rapidly under her breath, a broody symptom, and holding herself fluffed up with wings slightly out to her sides, another broody symptom.
When this behavior would annoy another hen who would give her a scolding peck, Saffron emitted a screech and would puff up and flap her wings in defiance, another broody symptom. Yet Saffron continued to lay eggs uninterrupted, and she never stayed long on the nest after laying. In a few weeks, this phase had passed, and Saffron never did go broody all the way.
If Saffron had gone broody all the way, she would have begun sitting on a nest and stopped laying further eggs. She would have plucked feathers from along her keel bone to create bare skin to make direct contact with eggs she would be incubating, creating the right temperature and humidity for embryo development. It is when a hen reaches this final stage of going broody that we know for sure this is what's going on, and then we can break her broody hormones by placing her in a broody cage with an open mesh bottom, the exact opposite of a warm cozy nest. The open mesh allows air to circulate, thus reducing the broody's body temperature, and this interrupts the broody hormones after about three days.
Since the broody hen must remain day and night in the cage until her hormones break, the cage must be placed in a safe environment where she won't get overheated or freeze, and it must be protected from predators. If a broody is coming from a below freezing environment, the cage must not be placed where the temp is much warmer or she will suffer heat sickness. You would need to give her a place where it's ideally no warmer than high 40s. This way she can go back to the freezing temps and still be acclimatized when her hormones have been broken.
Giving a broody any extra heat might interfere with the broody cage being able to break her, another reason for adjusting her environment to her needs.