They should be fine once they are fully feathered, but may need some extra warmth at night for a little while. Just depends on how draft free their area will be. I don't remember how long it took mine to fully feather, but I know it was faster than my layers.
I have only raised cornish crosses one time so I don't have as much experience! I just process my extra roo's from the eggs I hatch (except the silkies, I find them homes).
1. My birds were done in small batches of a couple here and there. I started at 8 weeks old and finished when they were...