Feral = under exposed to humans......

I would make sure there is plenty of warm blanket like items in the doggie house. She/he is most likely used to the cold - but would love something to keep warm with.....maybe some straw on the bottom and some polar fleece or wool blanket on top...something to cuddle in....once the cat can confine its body warmth, it should be fine.....

Keep us posted....

Can you make another little house closer to your house....such as a carton with blankets in it?