this is what we have going on it is a pretty "green" as it is all stuff we have around the house. This is the third group we have done in this manner, outside only in once or twice when it was VERY cold. Otherwise a little cardboard to block any wind (I agree with the earlier post, EXTREME attention to fire hazards) and they have done just fine. We have only lost 1 chick out of probably 20 total, and that one was within a few days of purchase.
I hatched 30 chicks. I have had them in their 330 sq ft. coop since they were a week old. I have a wire cage in the coop that I covered with blankets. The wire cage has a door. I leave the door open & above the door I have a 250 watt red light hanging. Depending on the weather I keep it turned off during the day. At night I turn it on They go inside at night & get in a big ball & sleep. They seem to feather out faster because they are living in the elements. During the day they run, fly around, get on their roost, take dirt baths etc. I think baby chicks can handle alot more than we give them credit for.
Farmers have done their brooding in barns since forever. Millions of chicks are brooded in barns, not in spare bedrooms or bathrooms.
Of course, you can achieve the required temperatures in the coop. You just use a box out there. You can cover 90% of the top of the box and that usually holds the temps inside well within the required parameters. We brood out dozens of chicks each year out in the barn. I couldn't keep the temps right in the dead of winter, but once daytime highs are in the low 60's and the nights no longer fall much below 40, you can easily do it outside. Warning: take all safety and anti fire hazard precautions no matter where you brood.
The dust these chicks produce is unholy and the smell, well it is organic, shall we say.
I'll just add to this.
If you have electricity there, you can do it. I'll repeat what others said. Be very aware of the fire hazard. If you use a heat source that comes with a clamp, throw that clamp away so you are not tempted to use it. Use wire to support it so it cannot fall, even if a grown chicken jumps on it and bounces up and down. Make it secure!!!
I keep my brooder in the coop from day 1. You do need to keep one area warm that they can go to to warm up when they need to, but I think it is healthier for them to be able to go to cooler areas when they want to. I keep one area in the right temperature range but the rest is a lot cooler.
I'm going to brood in the coop since it will be otherwise empty. I need to run a sturdy extension cord from an exterior outlet to the infrared heat lamp but other than that, no big deal. There are great instructions in a book I have (Storey's Guide to Raising Chickens) for how to set up an area brooder and it's absolutely fine to do that rather than setting up a box in your home. I'm fairly certain nobody used a plastic tote in their laundry room 50 years ago...