My Cochin went broody -- unexpectedly, as it had not been that long since her last broody.... So.. she went broody on Saturday, the 17th.
I guess I have a hatch date around the 7th of January.
To more address your issue... I think my Cochin went broody this soon again, because I had to end her last broody, due to the eggs being contaminated by worming meds... so, I was throwing away all the eggs. To end her broody, I took away the nest -- this was not difficult as I have three buckets in the coop, in the rather open nest boxes, due to the hens liking the privacy. (Five gallon buckets with a square cut in the side to open them up make a nice private nest.)
But, I was not successful ending her broody immediately -- she had sat on eggs, I took them away and threw them away, she still sat on an empty nest. Other hens came in and kicked her out, laid an egg of their own, and she sat on that... I kept taking eggs away and she sat on the nest with or without eggs until I took away the bucket nest ... all three of them. Then, a couple of days of sulking and trying... and she gave up and lost her broody.
Now, I am in Southern California, and though it is frosting at night, it's not like other places with really cold weather and snow. I am going to let her sit on eggs now and hatch them. I have not decided what to do after they hatch, they may need to be indoors, warmer than the coop.... not sure whether to put a heat lamp in or what yet.
I suppose if you can get rid of the nest completely, that would do it. Others have said, I have read that you can separate her, put her in a cage, where she does not have access to a nest, and it might take some time to break her broody.
I think that if you search "breaking broodiness" or "breaking a hen's broody" you will find more ideas on how to do that.
It just breaks my heart to do that, so, I will let mine sit now and figure out how to keep her and the babies more warm later, by the time they hatch.
Best of luck.... If she is like my Cochin and you break her broody this time, she will go broody again, sooner, probably before it gets warm.