Here's a link to the Green Pepper Patterns mentioned above:
http://www.thegreenpepper.com/adults.html
To answer your question - I was in on the fabric run that ZamIAm did a few years ago, which included a fabric lining on the backside of the neoprene. So, we didn't need to "line" the body suit fabric.
However, you do need to include a black undersuit below the crop-top as that does show where the vest comes together on the sides. For that I would recommend something that breathes - cotton.
I don't know about the neoprene you ordered specifically - JDFett would be the one to answer that. You don't want the stuff sticking to you forever! 
I understand your concerns about the heat... believe me! I'm in Arizona. I'm thinking along the lines of what the Vader's end up doing with water cooling - I have to research it more though. I'll let you know!
