The video card is in the CPU tower which is turned on.
I would not worry about anything running while monitor is off. As long as your tower is dissipating heat properly and most specially not much activity where it would most likely not create thermal events. I usually leave my desktop computer for 4 to 8 hours with monitor only off everyday. Just make sure to do the maintenance cleaning if you feel you need to.
Edited by jhayz, 12 December 2011 - 07:54 PM.