With the Single Sign On handler plugin system this could be easily accomplished. It will be included in eZ publish 3.8 ( http://pubsvn.ez.no/nextgen/trunk/doc/features/3.8/single_sign_on_handler.txt )
Unfortunately, I have to program this on eZ 3.7.2 on a project going on right now, so I have to figure out a different way to do this. Would be very glad to here more on alternative solutions :)
I am thinking on writing a Javascript in my "Pagelayout.tpl" that automatically sends in username/password, but I am not really confident if this is right solution.
You could try to backport the Single Sign On plugin system to eZ 3.7 ;-) It was committed on the trunk in SVN rev. 15462, and you only have to modify one kernel file, so I guess it's the most ez way.
