then I can still have a heat lamp should they need it.
Two things on this. If you do use a heat lamp use wire or chain to hold it in place. Do not use that clamp that comes with it, that clamp can fail or be knocked loose. Do not use string or plastic that can burn or melt, use wire or chain. That should reduce the danger from fire tremendously.
My 3' x 6' brooder is in the coop. I use a heat lamp to keep one end warm enough when it is below freezing but it is big enough so that the far end cools down enough when the temperatures get warm. To me, the temperature swings are the hardest part about brooding outside. I've seen it go from below freezing to the 70's overnight. I find that chicks straight from the incubator are very good about finding their comfort zone when given the option.
I've had chicks 5-1/2 weeks old go through nights in the mid 20's Fahrenheit with no supplemental heat. The coop they were in had great ventilation up high and great wind protection down low where they were, so the coop plays a part in that. But they were also acclimated after being raised in that big brooder in the coop. Some mornings I'd find ice in the far corner of their coop but the end they were on was toasty. They play in the cold and return to the heat when they need to warm up. It's not as simple as a certain age and a certain temperature, there are other factors like acclimation, ventilation, and wind protection. But 5-1/2 weeks and below freezing, They can be pretty tough once they feather out.
So do you guys think it would be too stressful on the little guys to transfer them into the dog run during the days, and back into their little enclosure in the coop at night?
Not stressful on them, maybe on you. What you might do to acclimate them is to take them outside when it is cold during the day or evening and expose them to the cold well before 5 or 6 weeks. Keep them out of a wind and watch them. They will let you know if they start to get cold. To me, there are several benefits to this. They get acclimated. You see how well they handle cold for yourself so it should help your confidence tremendously. And it exposes them to their future environment. They will peck at the ground if they can. If that is in the run they will get grit in their system, they will get probiotics from the adults, and it will strengthen their immune system by exposing them to any flock immunities they need to work on. I'd much prefer them to be exposed to those things while they are still in the brooder because it is so much easier to observe them in case there are issues. I believe in this so strongly that I start feeding my brooder-raised chicks dirt from the run on the second or third day in the brooder and repeat every three or four days. I keep my brooder very dry and have never had issues.
I understand you are worried, you should be. Bad things can possibly happen. But with your planning and the room you have I think you will find this to be a good experience.
