Not sure how they have set it up. Is the other one vBulletin? They have some funny cookie tricks.
There's no individual setting in your profile for this. Might be able to set it globally but frankly I'd rather not since I prefer to not be logged out when I have to deal with a dodgey connection or whatever.
Anyway, as you said...................
setting my browser to clear cookies upon shutdown.
Devious, treacherous, murderous, neanderthal, sub-human of the West.