Should I move the Broody and batch on day 20?

It got below zero (celcius) with snow here (SK, Canada), of course, after an amazing warm winter - just as hatch day is approaching. The broody is in a windowed/wooden/uninsulated "hutch" by herself, no heat or lamps added. She is a silkie, an this is her (and mine) first attempt. I gave her three eggs, and now there is five (until yesterday there was a silkie roo and another silkie hen in with her and I suspect these are the other silkie's). I candled the original three on day 11 and all was good, two for sure on day 18 were full of chick wiht a nice big air space! I don't know if I should move her, intact with nest box without touching anything, into the house or not. Would the sudden temp change from outside to house temp be bad or good? Opinions?? This is so exciting and frustrating at the same time. Tomorrow, none of my people better be making demands on my time haha!~ I will be stuck to the chicken area ...

 

Well, after trying to rig a lamp in the hutch she was in...I managed to get the whole setup inside a tack shed, and a much safer lamp situation. It was forecast to be -12C last night.
I picked up the whole nest box, with all contents and passengers, and moved into a large rubbermaid-type container. Last night at about supper time- FIRST CHICK!!! The hen never even budged about the move - not sure she even realizes in the trance she is in. Lockdown...no kidding!
Well, I 'm headed over to the raising chicks threads now! This is my first baby...it looks like the only purebred I put to hatching - a golden laced polish. No pics yet, don't want to upset the family (yet...)