Not really...
It is a complicated problem. You can read this:
www.tutwow.com/htmlcss/quick-tip-css-100-height/
an experiment here:
jsfiddle.net/compojoom/nKuhT/
I can easily set the map height to 100%, but then since your template doesn't have a height of 100% in the body and html, I'll pretty much make this div as big as itself - since this div is containing dynamic content and has nothing in it, it will end up being just 0px in height...
I just got another idea that is perhaps more interesting than this - maybe when the user clicks on the fullscreen icon we can add a variable to the url for full screen. So if the user sends a link to a friend, the page will load and hotspot will move to full screen. But i guess that maybe most of the users will want that the user looks at their cool logo instead of a big map...