I'll give you a link that talks about mama raising chicks with a flock. I'll admit it does tilt my way, but it does give you different opinions.
Raise with flock? thread
https://www.backyardchickens.com/forum/viewtopic.php?id=215937&p=1
I disagree that a rooster will definitely peck a chicken on the head. A good rooster will protect all members of his flock. Not all roosters are good, but there have been many posts where roosters have protected chicks from hens and have really helped the chicks when mama abandons them too early. And a good mama will keep a bad rooster away from her chicks. I can't guarantee you that bad things won't happen as yo are dealing with living animals, but nature's way is for a hen to raise the chicks with the flock.
A young chick definitely needs a mama to protect it from the rest of the flock. Any young chick is in danger if it does not have mama to protect it. Read the integration threads.
If mama is taking care of the chicks, you do not need to worry about temperature. She will take care of that. Hens raise chicks outside in freezing weather without problems. When the chicks get cold, mama warms them back up.
I do see a potential problem however. If you have 3 hens that are all hatching at the same time, there is a reasonable chance that one mama will want to take all the chicks to raise. If that happens, the hens will fight, possibly causing serious injury to one. Sometimes chicks in the area are accidently injured or killed in these fights. Another thing that can go wrong is that a broody will kill the other hen's chicks, either as they hatch or maybe a week later. I guess she sees them as competition for hers. If I had multiple broodies, which I will not allow to happen, I would separate them before the eggs start to hatch and raise them separately or give all the chicks to one hen to raise and break the other broody if the chicks are close enough to the same age.