I can tell you how stone or cinderblock buildings do for *horses* in the winter, which is much the same thing as for chickens.
They are real toasty warm for the first part of the winter, because of the great thermal mass involved (the walls themselves, and the ground they enclose, since IME they are invariably earth- or stone- or slab-floored).
In cold regions the thermal subsidy sometimes piddles out in mid to late winter leaving you with a really COLD building that doesn't even warm up in the daytime... depending on how cold your winters are and what exactly is the structure of your building (more massive or larger buildings, especially ones with many stone or cinderblock internal walls or partitions, will stay warmer longer than smaller or thinner-walled ones).
However if your "cold" winter temperatures are just in the teens F (like, *positive* teens) then you really need not worry about cold
What you WILL have to be careful of is condensation problems when you get a warm day in January and as spring approaches. Once the stone walls/floor have started to cool, if you then bathe them in a warm humid unseasonable Southern airmass you can get condensation to the point that the ceiling literally drips and all interior surfaces have a film of water on them. This, needless to say, is not so great for chickens
On days like that, if they are forecast to be brief and limited, it may actually be best to shut as much ventilation as possible. Although when you get a long spell of spring weather you sometimes just have to suck it up, throw alllllll the windows and doors open, maybe run a fan if necessary, and simply hope things dry out quickly (determined by the rate at which the stone/concrete warms up).
(
If you should find yourself having too many aggravating problems with condensation like that, you can insulate the inside or even just put a plywood lining on the inside walls. This is not a perfect solution but sometimes worthwhile. However your building is smallish enough and your climate sounds warm enough that I would pretty much doubt you'd ever need to.)
So on the whole, I think that as long as it is predatorproofed adequately you are likely to be very happy with your building as a chicken coop
You really ought to add some ventilation though. Gaps or cracks in the door are not adequate. If you can ventilate through rafter gaps that can work, or make some of the windows openable. (Are they really *all* plywood-ed over, with no natural light???)
Good luck, have fun,
Pat