Can I use steel framing in a shower enclosure
I've used steel studs in bathrooms many times. The temperature never seemed to be a determining factor.
I personally would hesitate using green board and would use one of the many cement board, wonder boards, that are out there. Structurally, they are much better than the green board and will last longer. Also think about using a water proof coating like Red Guard in the shower areas. There's no problem with adding sheet rock over sheet rock. Just go wall to wall for appearances. You'll need longer screws and will need junction box extenders for any fixtures.