I have had very good luck with getting them into the flock in a week at the age of 3-4 weeks.
Instead of using heat, I use insulation. I have a what I call a wooly hen, which is a box with thick wool padding on top. It is about 5 inches high on the outside, and three inches high on the inside. Chicks can get into it and out of it, on two sides.
I turn the heat lamp off at night. Then the first night or so - encourage then to go under the wooly hen. As the heat goes off, there is a lot of peeping. As they get settled in the dark, under the wooly hen, there is silence. They sleep all night. I checked with a thermometer and it was above 95 degrees in there. I do this the night I bring them home. I set them up in the garage, and have the heat lamp on during the day. But I shut it off at night.
I have the wooly hen in a dog crate. So they home to the crate and 'hen'. Then I take them down to the hen run, and set it up so that the chicks have a safe zone that the hens can't get into. I feed them in there, and they can go into the wooly hen if needed. At night they naturally go into the wooly hen, I close the door and place it in the coop, in the morning I carry it back out.
Day 3, I lift the barrier so that the chicks can get out into the run, and retreat to the safety zone as needed. I have a pallet up, not too far away, on low bricks - another safety zone where chicks can get out of reach of a hen.
Night 5 - I carry the dog crate into the coop, and leave it open. Usually by the next morning, they are out in the run with the hens by morning when I get down there.
One or more times of moving the crate, and then they figure where it is in the coop, and they go there themselves at dark, I do have ground floor door to the coop.
Works easy peasy for me. No heat lamps and no worries of fire.
Mrs K