No, there is no fan that runs when off. I have this in my bedroom as well, and when on, I don't hear a thing. Also, not sure if this in relevant for you, but some people say there is an audible "buzz" sound that comes from the tv when it's on. I do not notice a buzz except for when I have the image retention scrolling bar feature on. It seems to buzz when there are large amounts of white on the screen. The TV itself is amazing.
It is completely silent it does heats up but i guess not a problem cause i have done 8-10 continous hours of gaming and it does it like a pro i do not have a fan in my room. I will highly recommend this tv but this black friday i heard e8000 is bieng sold for 1200 which is even high top notch