Plenty of people hatch at this time of year without issue, so I don't think the fact that it's October matters. I'm assuming you mean +10 celsius for the temperature; a broody should have no trouble keeping them warm, especially in a polytunnel. And you said the broody successfully raised a...
OK. So let's turn attention to the chicks.
Were they home bred or did you buy in hatching eggs?
If home bred, were the parent stock related, and if so how closely? what were you feeding the birds whose eggs you set and the roo who sired them?
And what are you feeding the chicks?
Is there any chance the hen is ill? If she has an infectious disease that can be passed on in fomites (feathers, dander etc.), any chicks she's brooding are getting a massive dose under her.