Starting it up I wouldn't think require any "extra" fuel. I'm more concerned with the extra starting cycles on the starter motor.
That said though, I shut mine down if I leave the truck and it is not in the driveway at home.
However, back when I lived way farther north and the temps were down below freezing... . I left it running even if I was out of the truck for 15 minutes or more. doors locked of course (not that would matter to a thief)