"Part of the theory is that as the earth warms the water will expand and take up more room."

This isn't a theory, it's well known that water expands when heated. The term is Adiabatic expansion. It is responsible for ~1/3 of the observed global sea level rise. 

http://onlinelibrary.wiley.com/doi/10.1029/2012GL051106/abstract

I also want to point out that any floating ice which melts will have zero effect on sea level since it's already displacing an equal amount of water.