Well, it was a real nail-biter for me. I took away the heat lamp at 3-1/2 weeks and put my 4 red pullets and 2 bantams in the outdoor pen (equipped with just a small used resin doghouse) at 4 weeks. The first night was in the high 50's and they did great. On the third night, the temp dropped to a crisp 26 and they survived. This morning, it was 28 and they were out in the open air section frolicking and having a blast! They are only 4-1/2 weeks old.
I'm not saying that this fits your scenario. Mine still have a teeny weeny bit of fuzzy stuff on them, but they really feathered out fast. They were a week old when I brought them home. I put them under a 40 watt bulb, about 10 inches above them. After a week I replaced that with a 25 watt bulb. After a few days of that, they didn't want to sit under it anymore, so I just got rid of the lamp. They sat in my basement at 55-60 for a few days until I got the pen ready.
I spent too much time and energy last year obsessing about keeping the flock warm. IMO, they are much tougher than we give them credit for. Just get a feel for when they outgrow the need for artificial heat. If they don't sit under it, they don't need it. They certainly surprised me.