Honestly... you being worried about everyone else's electric bill is touching... but... I gotta disagree on this idea. My pc doesn't 'overload' while playing XIV, and I normally have a few browsers up and maybe another game at the same time.
Just because I'm 'afk', does not mean I'm actually away from my computer. I could be looking up/comparing items, or working on the linkshell website going back and forth for input (which sometimes I'm 'afk' for 30 minutes to an hour, maybe less, maybe more). Even if I'm on the game all day, I generally stay in the inn so atleast the cities have one less person standing there.
If I had to log in every time because of an auto log out feature... I'd be pissed off to high heaven. No offense to the OP...
I will say this, I do log out... when I sleep. I don't stand there showing off awesome armor/weapons like many do. There's my good deed at energy saving.
Props for the touching thought though, really. ^^b