It's hard to say.. It seems that many of the accounts I've read involved enclosed areas - like Todd's hen incubating in the top part of the coop. The last one I read about was in a large, aviary-like enclosure and had the nest in a bucket that was laying on its side. Do you just have that one hen with a roo? I believe I did read an account where a hen got broody after being placed alone with a roo, but if he stresses her, it's not likely to happen.
It seems to be important that the hen is not stressed by people either - maybe that's where the enclosed area comes in, so she doesn't see the person feeding her. Don't know whether Todd fed them in the top part of the coop, though. But if possible, I'd add more than just the log - plants, perhaps. And if you have an old bucket or a broken flowerpot, I'd add that too. And if the cage is very open, I'd place some sheets of wood around it, so at least some of the cage becomes a little dark and more protected..
Just guessing though, never even had cots ^^