You need not worry about the rear end temperature, they normally run in the 140-150 range.
Yes it is a good ideal to paint all the surfaces that Dodge and there cheap accountants failed to do. I think people are getting less and less truck for there money, any area that they can save . 20 on, isn't safe. The rear end cover and differential housing both front and rear are both in need of a paint job. The drive shafts always bothered me, I just can not see letting them rust away. Same goes for the hitch in the rear, they rust up in no time and many one this forum have experienced failures, wonder why?
Yes paint the trany, mine was painted for me by the good folks at ATS, it's a brilliant combo of pink and purple. It looks great next to the blue drive shafts and polished mufflers.