I don't know how you are planning to set it up, but be very careful to not start a fire. Very careful.
I have not started them in quite those temperatures, but it has been down in the upper 40's not long after I started them and I brood in the coop. I have a fairly large brooder. 3' x 5', and keep only one area in the correct temperature range. The rest is allowed to cool down to ambient. When I hatch chicks and put them in there, I find that they tend to stay around the heat for a day or two, then start running all over. With shipped chicks, they seem to start running all over a lot sooner, probably because they are a day or so older. I don't try to keep the entire brooder the perfect temperature. Outside with the changing temperatures that would drive me crazy trying. I'm sure I could not do it. I do think they are better off with that variety of temperature too, helping them get acclimated. So I heat one area to the "right" temperatures and let the rest cool off. That way they can find their comfort zone in case the heated area gets too warm. You might be surprised how little time they actually spend in the warmer zones.
One thing you need to be careful of is wind chill. Make sure they are not in a draft. I put a draft guard around the lower 12" or so of mine to make sure. I use a piece of plastic that you would use as a paint drop cloth for mine.
If yours does cool off away from the heat source, you might want to put a temporary barrier around the heat the first day or two to keep them near it until they learn where the heat is. But make sure it is high enough that they cannot jump out and get stuck away from the heat.
I also have plenty of ventilation up high in my brooder. I'm a believer in keeping the wind off of them but make sure they have fresh air to breathe.
I suggest you set it up well ahead of time and try it out. Put a thermometer on the bottom of the brooder and see what temperatures you get in various areas under different conditions. They do need a warm place to go to, but the entire thing does not need to be "warm".
Depending on what your coop looks like, size and draft free, you might not even need a brooder all that long since you don't have any adults in there. If you coop is pretty well protected against drafts, especially on the ground level, you might consider letting them out of the brooder earlier than we normally do, just heating an area for them to go to.
Raising them the way I do, I had 5-1/2 week olds in my grow-out pen with no heat but good draft protection when temperatures got down into the mid-20's. They were already acclimated and there were 14 of them, so they could help keep each other warm.
Here is what my set-up looks like. That top is because I have adults in there and I want to keep them away from the heat lamp. With my first batch, that top was not there, just wire.