I just went through this with 25 of my own. To be honest, after 2 weeks I sold 9 off, but I totally understand your situation. No rubbermaid container or cardboard box will do, nor is it fair to the young chicks who need to literally stretch their wings and run a bit. Also, after a couple of weeks with 25 chicks, I know how freakin' dusty they can make things. So...I am hear to give you the answer to your dilemma. Are you ready?
You've got a couple of choices. I did both of these:
Firstly, I built a half-way house. I took our patio dining table, moved it into the garage, and then took blue plastic tarp and draped it over the entire table top, and three sides. I ducked taped it to the floor in a few spots. I then put several layers of cardboard (the old cardboard that made up the walls of the first brooder which I kept in the living room) on the floor, so the chicks wouldn't have a non-insulated floor. Over that I draped plastic, and over that a deep bed of straw. On the open side, I put some chicken wire. I used strong spring grips to hold it in place. Inside this brooder were two lamps for heat. On top of the table I placed several blankets to act as ceiling insulation. So...at two weeks, I moved my 16 chicks out into this half-way house. It was in the garage, and I could readily check on them. Of course I was scared that it would be too cold (our nights regularly hitting 32 degrees here in Southern Oregon). But, they were fine. On night one, I got up at 2am to check on them...all were sleeping comfortably. In short, I had created a nice warm environment where the heat was retained. Oh...one more thing: that open chicken wire end wall, I'd drape a couple of towels over that at night, to keep the heat in there too. You can adjust these to regulate heat.
Secondly, after two weeks in the half-way house, I moved them all into their adult coop (see pic link at bottom). Now, all I did here was to take those same pieces of cardboard on the floor, and recycle them one more time. This time, I made an area inside the coop where I could trap in the heat with the cardboard. So, I duct taped the cardboard to form three walls. I placed it underneath what will become the girls roost boards, and on those boards, I hung the two heat lamps. Over the roost boards I put the "ceiling" cardboard. Viola, another micro climate where you can control the temp.
I know we worry that our little chicks are too young and frail to go out in a garage or coop. The truth is, you can make that external brooder environment any temperature you want! It just takes proper heat lamps. It is imperative that your test first with a thermometer! Give them more heat than they need, and a place for the excess heat to escape (as well as the girls to move away from it) and they will wind up placing themselves in their own comfort zone. So, don't forget, the chicks need room to move away from the heat too. I see some pics of these rubbermaid brooders where I fear the chicks will become little rotisserie chickens before their time!
Good luck. I hope this helps.
Brian