A quick and simple fix for this can be found on webupd8.
To test this quickly without much work, just launch:
gnomesu gedit /usr/share/themes/Adwaita/metacity-1/metacity-theme-3.xml
Now find this next line, Ctrl+f to search, you want to be sure it is the line that reads
change that so it looks like this:
frame_geometry name="max" has_title="false"
Now restart the shell to view the changes, Alt+F2, type
r, and Enter/Return.
To further customize this you should examine the above webupd8 article and make your changes carefully, or paste the entire contents of the
frame_geometry style including everything between:
<frame_geometry name="max"...> ... </frame_geometry>
As you will see with the above edit, the entire title bar isn't gone, a small portion remains. But I did not make the other changes and the contents of that stylesheet differ between shell versions, read below for another change I tested. I am also running 3.8 though, so I went ahead and did some testing and I made one more change under
frame_geometry=max I changed the following value from 8 to 0:
<distance name="title_vertical_pad" value="0"/>
You'll notice the difference now, and there's still a bit of a shadow left over, but it actually looks pretty good to me.