Fred's Hens :
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.
The three things to provide:
1. An area in the right temperature range.
2. Draft protection. No breezes on then at all.
3. Predator protection.