Featherless Finch baby

Question
I have had many baby finches but this last one that was born is growing bigger....but has no feathers on its body and no tail feathers either.  It only has feathers on its wings. I don't care that it looks bizarre...but can it survive without feathers. It seems afraid to even leave the nest..

Answer
Did it have pin feathers earlier on? If so, someone had been picking on the little guy. If not, I don't know what to say. It could be a birth defect but I suspect someone is pulling at him.
If you keep the temperature up in the cage at a constant 31C for the little guy he should be okay. No drafts no anything that could get him sick for he can get way sicker way easier than other birds.