What you plan to do is really close to what I do, even to the point that the top of my 3’x6’ brooder is my droppings board. I’ll enclose a photo. I use heat lamps but the heating pad cave is real popular with many people right now. Others use emitters or something else as a heat source. I put chicks in there when the temperatures are below freezing (have some eggs in the incubator right now) or in the heat of summer. In the winter I really wrap this well, in the heat of the summer it’s more wide open. There are lots of different way to do this.
What you are trying to achieve is to provide one spot that is warm enough, but let the rest cool down as it will. Even straight out of the incubator my chicks are really good at self-regulating temperature if given a choice. And they will play in pretty cold areas with no problems as long as they have a warm place to go to. That’s how a broody hen operates. She does not heat the entire universe, just gives them a place to warm up when they need it.
One of your issues brooding outside is that the temperature varies, sometimes a lot. It’s practically impossible to keep the entire brooder one perfect temperature, which by the way does not exist. Just like people, some chicks prefer it warmer, some cooler, but they can operate in a range of temperatures. By providing a spot warm enough in the coolest temperatures and a spot cool enough in the warmest temperatures they will take care of this.
If you are brooding when temperatures are below freezing, you need a way to keep water thawed. I just put my water in the warm zone. Others may use heated waterers or some other method. Or just wait until the danger of freezing is past.
I also have concerns about how much room you have. To me, the most important part of integration is providing them plenty of room. The chicks need to be able to get away from the adults. Until they mature enough to force their way into the pecking order (usually around the time pullets start to lay for my pullets. It’s hard to generalize for cockerels) the chicks pretty much form a sub-flock and just avoid the adults. If yours can free range they should be OK, but don’t leave them locked in that coop together in the morning after they wake up until you are confident they will be OK.
I do mine two ways. Often for my own reasons I put them in my grow-out coop at about 5 weeks and at 8 weeks open it up for them to roam with the flock. They will then put themselves to bed in that grow-out coop. But sometimes I just open the brooder door at 5 weeks and let them mingle with the flock. I have an 8’ x 12’ coop, a 12’ x 32’ main run, a 4’ x 8’ grow-out coop with run, and about 45’ x 90’ inside electric netting. Mine don’t free range but I have a lot of room. I have never lost a chick to another adult chicken doing it this way.
Cafarmgirl, have you ever seen a 10 week old chick stand up to and fight an adult? I never have, mine always run away. My pullets won’t do that until they are pretty mature, usually when they start to lay. Who can say about cockerels? I’ve had some scuffle hens at 4 months, some running from hens at 11 months. I’m not trying to criticize your choice of 10 weeks, it obviously works for you and is best for you. I’ve just never seen a 10 week old chicks stand up to adults. A lot of people quote 16 weeks. I’ve never seen a pullet stand up to a hen at 16 weeks either. I do think the less room you have the older they should be when you integrate.
Some of the things that I think help integration go smoother regardless of age difference are to house the chickens where they can see each other and get use to each other without getting to each other, give them as much room as you possibly can, give them safe havens (Azygous has a good one, but roosts high enough that the young ones can go up there out of reach of the adults or places to get out of line if sight are also helpful), provide multiple feed and water stations so they can eat and drink without challenging the adults, and don’t force them together. Let them manage how close they want to be to each other. When they mature enough they’ll merge into one flock.
A lot of times these integrations go so smoothly you wonder what all the worry and fuss was about, even when you don’t do everything “right”. But occasionally you can have disasters. Doing these things will help improve your odds of success but with living animals you don’t get guarantees, one way or the other. And we all have different experiences. What works for me might not work for someone else. We are all unique, with our own set-ups, goals, and management techniques.