I know I'm late to this convo, but given the choice, I'd let a broody incubate and raise the chicks over doing it myself. A good broody is an invaluable asset, and unlike me, she can devote all of her time and energy to teaching and integrating the chicks. The chicks we have that were raised by broodies are far better adjusted, outgoing, and active than their human-reared counterparts. They were fully integrated into the flock at just a few weeks of age, thanks to their sassy mama's protection, meanwhile 3-month old "chicks" we'd gotten in September were still outsiders to the flock. Like others have pointed out, you want to make sure she's truly broody before you plunk eggs under her, but if she's ready to go, I'd let her.
And as for the temperatures, depending on where you live, it may not be cold enough to necessitate bringing her indoors. Our broody Anna managed to hatch out four perfectly healthy babies even with below-freezing temps outside.