Mange is highly contageous so I'd be very careful who/what you handle after being around him.

As far as the temp goes, I would think if he's from that area and has been coming and going then he probably has a drey to be going to keep warm at night and will pull up more leaves or w/e if he knows he's been cold.

Nibblette used to remake her nest several times a week. Pushing stuff out pulling stuff in. If we turned on the AC she'd build it more, if it was hot she'd come out and lay on a platform or empty her nest.